It made me start wondering if your rival in the game (red/blue), or if he appears in the manga, is different from Gary. So are Gary and Blue the same? If not, what are the major differences?
The different versions of Pokemon (anime, manga, games) are mostly inconsistent with each other, and aren't directly comparable. Here are the versions of this character:
- Blue Oak from the games is the rival of Red in Generation I (as well as Leaf in the Generation III remakes), and is the gym leader of the Viridian Gym in Generation II and the Generation IV remake. In the games in which he is the rival, you have the choice of his name, and "Gary" is one prerecorded choice that you could make. His Japanese name is "Okaido Green" (オーキド・グリーン).
- Blue Oak from the Pokemon Adventures Manga is a main character and Red's rival. He is based on Blue from the game. Being a manga, he obviously isn't nameable. His Japanese name is "Okaido Green" (オーキド・グリーン).
- Gary Oak from the original anime is one of Ash's rivals for the first few seasons of the anime. He is also based on Blue from the game. Again, since it's an anime he isn't nameable. His Japanese name is "Okaido Shigeru" (オーキド・シゲル)
There are definite similarities between all three of these characters. For instance, all of them are the grandsons of the respective Professor Oaks. All three are the rivals to the protagonist. All three are respectable trainers, and in many cases they have some of the same pokemon.
However, there are quite a few differences as well. For instance, Gary competes in the Pokemon League in 3 regions before going to work as a researcher. Blue from the game becomes the League champion, only to lose to Red, after which he becomes a Gym Leader. Blue from the manga doesn't even collect gym badges; he's only acquired one. The Bulbapedia pages above contain much more detail, but the point is that these three characters are quite different in personality, style, and story, so you really have to regard all of them as different characters who just all happen to have similar design and occupy similar positions in the stories.
Incidentally, there are other characters named Blue as well (taken from this Bulbapedia disambiguation page):
- Blue from the Pokemon Origins Anime is based off of Blue from the original games. This series seems to be following the game story reasonably closely and the characters are quite similar. His Japanese name (at least so far) is just "Green" (グリーン).
- Blue from the Pokemon Pocket Monsters Manga is again a rival of Red, but clearly a different character, as evidenced by the fact that his Japanese name "Blue" (ブルー) doesn't match the others. The character based on Blue in this version is Green (グリーン), whose full name is "Midorikawa Kai" (緑川 開)
- Blue from the Pocket Monsters Ruby-Sapphire Manga is based on Leaf, not Blue. She is still a rival of Red. She doesn't seem to have any relation to the original Blue, and her Japanese name Midori (みどり) is different from the other characters, though it could be translated as "Green".
- Green from the Pokemon Adventures manga is based on an unused female character design from the first game, which was also the basis for Leaf in the remakes. I've included her only because her Japanese name is "Blue" (ブルー); she and Blue switched names in the English version of the manga.
No, considering that one would be talking about Blue from either Pokémon Special, the games, or Pokémon Origin. Gary is also a name you can choose for your rival in the games, making the gameverse Blue/Gary comparison irrelevant, due to the fact that it is one's own choice. Gary is mainly known from originating from the anime as Ash's arrogant rival, accompanied by fangirls and cheerleaders. Blue, or Green in Japan, from Pokémon Special/Adventures is the more mature, and serious counterpart to Gary and Blue from the anime and games respectfully. He is Red's rival in the manga, and is considered by Red himself to be a rather powerful trainer. Blue from Pokémon Origins would also be rather irrelevant, since Pokémon Origins is based strictly off of the events in the games.
Basically, there are three arrogant rivals (One maturing a little in their respective series((Gary)), and a serious one.
Yes, they are the same character. You get the same name suggestions for them in the red/blue games themselves.
Nintendo Power use to refer to your rival as "Gary", and it would probably have referred to you as "Ash" if it ever talked about "you" in the third person, and it did so as long as I've owned the magazine (late 90s early 2000s).
Both "Blue" and "Gary" were the grandson of professor Oak, too, so they definitely are the same character, and to that point, their rivals (Red/Ash) are the same character too.
*One point of interest: if you played the "cold" version of the game (Blue), then your character would be suggested as "Gary", and your rival would be suggested as "Ash".