I know that the actual characters who are the homunculi differ between the FMA manga and original anime. For instance, Sloth is a different person between the manga and the anime. However, do they differ in how they are created? If so, how do they differ?
The following contains heavy spoilers for both anime watchers (up to roughly episode ~48 in the 2003 anime, and roughly episode ~40 in 2009 anime) and manga readers (up to chapter ~75), telling about who, how and when created the Homunculi. I mean it.
In manga and 2009 anime, the Homunculi are
spawned by Father, who himself was the earliest Homunculus that is known. After he consumed half of population of Xerxes, he became some sort of a philosopher stone, and was able to create his so-called "children". He made each of them from one of his vices, and named accordingly. Each Homulculus is powered by a Philosopher's stone, which gives them the energy to live. (1)
In the original anime (2003),
Homunculi have different origin. They appear each time an alchemist performs Human Transmutation. Usually, the result of Human Transmutation will be a failure - a monstrous corrupted agonizing creature that dies soon after it was created. However, if a Homunulus is able to contact with a Red Stone, they can consume it's power to reshape their bodies. (2)
The difference of Sloth in manga/2009 anime and 2003 anime is caused exactly by the reasons above, because in 2003 anime
Sloth was created as a result of a failed attempt to revive Trisha - Ed's and Al's mother. She was fed Red Stones by Dante until she regained her original form.
(1) chapters 31, chapters 74-75
(2) 2003 anime, episodes ~45-48
Lust, Gluttony, Envy, Pride, and Greed are the same in both. The only differences are Wrath and Sloth:
In the Manga, Bradley is Wrath. However in the Anime, Izumi Curtis' son is Wrath. In the Manga, Sloth is the huge and ugly guy, whereas in the Anime it is the beautiful lady (sorry, I haven't finished the anime so I can't give more details).