Although this question was closed, it was actually through it that I came to realize that the anime and manga versions of Death Note are different, having only seen the anime version.
Just how different are the two versions?
Does the anime simply omit some details, shortening the story?
Or do they take completely different directions at some point? (much like the FMA manga and its first anime series) If this is the case, at which point do they part?
There are some minor differences.
For example, when L loses his life in the Anime, he doesn't say anything. But in the Manga he says something like "I knew I was right".
But the main difference is the ending.
In the Anime
Yagami Light, Near, Matsuda and all the squad are in a sort of warehouse. When Light tries to get the piece of paper of his Death Note from the watch, he gets shot by Matsuda in non-fatal points, both times. While the other guy kills himself, Light runs away, and ends up in another building of what looks like an industrial area. Ryuk is on top of a chimney and speaking to himself, he "reminds" Light about his first promise, i.e. that he would be the one to write Light's name on the Death Note. And that's what he does.
In the Manga
Light is still in the warehouse and he sees Ryuk (Near sees him too since he has the Note as well) and he begs the Shinigami to write their names. Ryuk says "Ok Light, I'll write..." and while everybody tries to shoot him, he adds "...your name, Light." Light doens't want to believe it but when Ryuk shows the Note, his name is written there. Light sees his entire life and remembers the same sentence Ryuk told him when they met (i.e. that he would be the one to write Light's name on the Death Note). Ryuk adds "it would be hard to see you in prison and your life is over anyways" or something similar. After 40 seconds, Light dies in front of the two detective teams.
Summary
There are a lot of differences between the Death Note Manga and it’s Anime adaptation, but they’re mostly minor differences, with the overall story being the same. Compared to the Manga, the Anime has had some scenes removed, new ones added, and some included scenes have been altered. I’ll go over some of the more notable changes, but this won’t be a complete list.
L/Light Arc
The conversation between L and Light that happens in the coffee shop was altered significantly, with the Manga scene being a lot longer and containing more dialogue between Light and L. In the Anime the only question L asks Light is the one where L gives Light pictures of the “L, do you know that Gods of Death love apples?” messages. In the anime L also asks Light what he can conclude by L revealing himself, and also asks him a question about the various FBI detectives that were killed by Kira.
The following scene, with Light, L, and Soichiro, had alterations as well.In the manga L asks Light what he thinks Kiras personality is like, which leads L to state that the most likely person to be Kira based on Lights description would be Lights sister, Sayu. This causes Light to be outraged, and Soichiro to state that he doesn’t believe it’s possible for Sayu to be Kira (but doesn’t make the same statement about Light, which is something Ryuk makes note of).
In the Manga the first meeting between Misa and Light contains an explanation from Misa about how much of a persons face she needs to see in order to know their name, which was omitted from the Anime.
Business Arc
The anime also excludes a few scenes between Rem and Higuchi, likely to prevent the watcher from discovering who the new Kira is too long before it’s revealed (due to recognizing the voice). The most notable exclusion is a scene where Rem tells Higuchi he can stop killing criminals now, but Higuchi refuses, stating he still needs criminals to die, since it’s good for business.
The manga also shows that Rem is disgusted by Higuchi and the other members of the “Kira board”. Rem tells Misa during their bathroom scene that her disgust at the actions of the “Kira Board” have made her come to the conclusion that Light may actually be a good person, and wishes for him to succeed (and, for this reason, is no longer able to kill people in order to help Light succeed, since it would cause Rem to die).
When Light gets the notebook back, and Misa resumes her duties as the second Kira, there’s a scene in the Anime which shows Misa walking in the city singing. This scene isn’t present in the Manga, and was added to the Anime.
The death of L is handled differently as well. In the Anime there’s a scene which takes place on the roof of the task forces HQ, after which L gives Light a foot massage. Immediately after this scene L and Watari are killed by Rem. In the Manga the rooftop scene and foot massage are completely omitted. The scene before and after this, showing that Rem is considering killing L to save Misa, is all just one scene. It’s not broken up by anything in the middle. When L does die, he’s complete silent in the Anime, but in the Manga he says “I wasn’t wrong”. Finally, there’s a few scenes between L and Watari in the anime (flashback to L at the orphanage and L coming to Wataris computer room at HQ) which aren't present in the Manga.
Near/Mello Arc
The second half of Death Note, featuring Near and Mello, contains a lot of alterations as well, with quite a few scenes being removed. It also adds a few additional scenes between Misa and Light, giving a bit more of a glimpse into their relationship, and expanding some more on Misas character (you really get to see how much she cares for Light, and how concerned she gets when Light is upset).
In the Manga Near brings Soichiro in for questioning after Near sends a chopper to pick up Soichiro in the desert. The SPK also gets the USA president to send in a squad of soldiers to retrieve the Death Note from Mello, but the assault fails due to Sidoh taking off everyones helmets so Mellos group can kill them with the Death Note.
In the Manga Mello and Halle Lidner are shown to have met prior to the scene where Mello puts a gun to her head, and almost immediately after the meeting between Mello and Near, Mello contacts Mogi and sends him to meet near. Near asks him a few questions and shares some information with him, with Mello and the task force listening in (although Mogi doesn’t say anything). Mogi is actually still with the SPK when Demegawa storms their headquarters, and safely escapes with them. Mogi is still with the SPK up until Aizawa goes to meet up with Near, at which point Mogi and Aizawa leave together. In the Anime Mello never contacts Mogi, and Mello and Halle weren’t shown to be in contact prior to Mello putting a gun to her head. When Aizawa gets in touch with Near regarding his doubts about Light he does it over the phone, and not in person. Interestingly enough, though, the Anime scene where Aizawa does first meet Near in person was actually over the phone in the Manga, so they (sort of) swapped those two scenes.
The anime removes a lot of scenes between Misa giving up the Death Note and Light making contact with Mikami as well. In the Manga we actually see Light looking for someone to replace Misa, and notices Mikami during a broadcast of Kiras Kingdom, which results in Light sending Mikami the Death Note. Mikami also tries to reach out to Kira (Light) during an episode of Kiras kingdom, stating that if Kira can’t get in touch with him he’ll begin acting on his own. Mikami also doesn’t get in touch with Light until the second meeting between Takada and Light. In their first meeting Light gets Takada to make some statements during the broadcast in an attempt to have Mikami contact her, and then Mikami contacts her during the second meeting between Light and Takada.
In the manga we see a few more scenes of Mello and Matt (the one who helped Mello kidnapped takada) observing Misa and Light, but nothing really notable happens in these scenes.
Ending
As the other answer already made note of, the ending is changed as well, and is definitely the biggest change. In the anime Light escapes from the warehouse after Mikami kills himself, and dies when Ryuk writes Lights name in the Death Note.
In the Manga Mikami doesn’t kill himself in the warehouse, and Light doesn’t escape. Instead, after Matsuda uses Light for target practice, Light crawls on over to Ryuk and begs him to write everyone’s name down in his Death Note. Instead Ryuk writes Lights name in the Death Note, resulting in Lights Death. The story then cuts ahead a few years, and there’s an epilogue. In the epilogue we learned that Mikami killed himself in prison, and that Aiziwa has taken over as head of the Japanese Police. Near has taken over the position as L, and still works with the police. The final shot of the Manga shows that people still worship Kira, and pray for him to return one day.
Misc
The Anime also contains a lot more imagery than the Manga does. In the anime there are several scenes which often don’t show what’s actually happening when some characters are talking. For example, during the “I am in Japan” conversation between Near and Light it shows the two of them going up a construction elevator, whereas in the Manga it just shows them talking over the phone. These changes were likely made to make the long dialogue scenes of the show more visually interesting.
In Closing
So that should cover the majority of the changes between the Manga and Anime, although I may have overlooked something. As you can see, the overall story remains the same, but there’s definitely enough differences between the two make reading the Manga worthwhile if you’ve already seen the anime (and vica versa).
Most of the major ones have already been brought up, but there are several small ones that make things change in ways you wouldn't expect. The easiest to see example is that Mello (in the manga) had a cross, both on a necklace (potentially a rosary or a fifteen-decade rosary) and hanging off his gun, in the anime the gun has nothing hanging off of it and there is no horizontal bar on the necklace. To most, these are minor, but the connotations are huge. Death Note had, over and over again, shown that there is no afterlife, that everyone returns to nothingness. We, as viewers, accept that that is the way it is in Death Note, but to the other characters, they would have no way of knowing. To me, such little things made a big impact from a lore and world building perspective.
For an interesting subtle difference, see the essay Two boys, one post? Or why anime Light is not the same as manga Light by casuistor, which goes in detail about how anime-Light and manga-Light actually differ in characterization.
Some highlights:
So before reading any of this, you may be thinking that manga-Light and anime-Light are fairly similar and they are at least superficially. Otherwise, their respective characterizations are quite different. This, unsurprisingly, gets established right from the beginning of both the anime and manga when you look at Pre-Kira Light.
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Manga-Light, for all intents and purposes, comes off like a relatively ordinary guy who jokes around with friends. Anime-Light IS the stereotypical loner character who shuns the company of other people. The anime even gives us a montage in Episode 3 to demonstrate exactly this point.
Here’s Light walking to school alone.
Here’s Light eating lunch at school by himself.
Here’s Light being too good to be a team player in a team sport.
Anime-Light well and truly physically distances himself from other people. It isn’t just emotional distance. None of these shots above are consistent with the friendly social mask manga-Light clearly puts on for the public.
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Another interesting difference to note is the way manga-Light is actually talking out loud when he’s chattering about the death note. It isn’t part of his internal monologue because it isn’t a secret. Anime-Light on the other hand examines the note and his thoughts stay internalized.
Anime-Light’s first sign of finding the note genuinely amusing happens when he picks up on this potential application of the note.
Taking into context anime-Light’s misanthropy, already eyebrow raising humor like this becomes even more alarming. Think back to all those classmates anime-Light is disgusted with. You can very easily picture a list of people anime-Light would consider toying with.
But if that weren’t weird enough, anime-Light has this inexplicable need to say this particular thought out loud. He’s within the privacy of his own room, of course, but it strikes me as unusual that he reads all of the rules in silence, and then feels the need to physically announce that he could theoretically make someone suffer.
Contrast this with manga-Light.
You’ll note that manga-Light keeps the same thought to himself. His dark humor (because that’s what it is) is for his own amusement alone and stays private and separated from the casual sense of humor that he would verbalize and share with the world. This is a distinction that isn’t present with anime-Light.
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In short then, the two iterations of Light Yagami are fundamentally different in their psychological make up. To use a glass analogy, at the start of canon, manga-Light is a perfect sheet of glass that shatters into pieces once he finds the death note. Anime-Light however, is characterized as broken fragments at the start of canon that are put back together when he finds the death note. This difference is even highlighted by the titles. The manga’s first chapter is entitled “Boredom,” Boredom is what compels Light to write in the note initially and boredom is what destroys Light’s personal mythos.
In contrast the first episode of the anime is called “Rebirth.” From the chaos that the death note introduces into Light’s life, we have a metaphorical rebirth. The glass fragments stitch back together to re-create an imperfect but unbroken sheet of glass as Light discovers his true purpose and embarks on his destiny.
Subtle, as I said, but fascinating.
