Blue is differentiated from Red/Leaf by Professor Oak's notion at the end of the Generation I games and Generation III remakes that Red/Leaf cares for Pokémon better than Blue does. This is also evident as Blue leaves the Silph Co. building while it's still under Team Rocket's control, leaving Red/Leaf to take out Giovanni.
He is notable for being cocky and arrogant whenever the player's character encounters him; after losing, his typical way to bid goodbye is "Smell ya later!"
Blue's name is Rival in this game. His team depends on which version the player has plugged in, and which starter Pokémon was chosen in that version. If there is no game inserted, he will always have the team in Case 1.
Before the Champion battle:
Hey! I was looking forward to seeing you, player! My rival should be strong to keep me sharp! While working on my Pokédex, I looked all over for powerful Pokémon! Not only that, I assembled teams that would beat any Pokémon type! And now! I am the Pokémon League Champion! player! Do you know what that means? I'll tell you! I am the most powerful trainer in the world!
After being defeated: NO! That can't be! You beat my best! After all that work to become LEAGUE champ? My reign is over already? It's not fair! Why? Why did I lose? I never made any mistakes raising my Pokémon... Darn it! You're the new Pokémon League Champion! Although I don't like to admit it.
Pokémon FireRed and LeafGreen
Before the Champion battle:
Hey! I was looking forward to seeing you, player! My rival should be strong to keep me sharp! While working on my Pokédex, I looked all over for Pokémon! Not only that, I assembled teams that would beat any Pokémon type! And now... I am the Pokémon League Champion! player! Do you know what that means? I'll tell you! I am the most powerful trainer in the world!
After being defeated: NO! That can't be! You beat me at my best! After all that work to become LEAGUE champ? My reign is over already? It's not fair! Why? Why did I lose? I never made any mistakes raising my Pokémon... Darn it! You're the new Pokémon League Champion! Although I don't like to admit it.
Trivia
Gary Oak from the anime was designed after Blue. Furthermore, Gary's name comes from one of the optional names for Blue. Despite this, they are not the same character, not even in Pokémon Yellow.
Blue is the only Champion who is the player's rival. He is also the only Champion that the player has battled before, as well as the only Champion who does not induct the player character into the Hall of Fame (Prof. Oak does it instead).
Blue is the only Gym Leader not to have a type theme.
It is a mystery who Blue's predecessor as Champion was.
The third generation is the only game both to feature Blue as champion and to not give him a specific sprite for his champion battle.
In other languages
French: Blue
German: Blau
Italian: Blu
Spanish: Azul
Chinese: 小緑Xiao Lou
Korean: 그린Geurin, Hangul phonetic of Green