The Pokémon franchise is home to many stories with many characters, but two of them, Blue and Gary, look so alike and fill such similar roles that many fans ask if they are related or supposed to be the same person. This confusion is understandable, as both served as the initial rival for the main character, and both were the grandson of Professor Oak. Blue and Gary's case is very similar to Red and Ash's; however, this one takes a bit more thinking to help distinguish.
Blue is the first rival in the Pokémon game franchise and eventually becomes the champion of the Indigo League. However, Blue is dethroned shortly after by the player and eventually takes the job as the Viridian City Gym Leader. After Pokémon Red & Blue, Blue shows up in later games for players to challenge as one of the most influential trainers in the world. Gary is the first of Ash's rivals in the anime series and remains so throughout the Kanto and Johto region. However, after losing to Ash in the Silver Conference, Gary turns his goal in life to becoming a Pokémon Professor, appearing throughout the series a few more times to show his progress in that endeavor.
Blue and Gary look exactly alike, which often raises the question of their relationship. The most likely answer is that they are the same person, but since they are in different continuities, they can live different lives. This is similar to how Ash and Red are the same people with different lives, but if Ash was a silent protagonist for an anime series, that would be a considerable hindrance to the writing of the show. Blue was a rather well-liked rival for the first games, so bringing his energy into the anime makes perfect sense to help bring popularity to the show. That decision paid off well, as Gary continues to be one of the most important and fan-favorite rivals of Ash's that helped push Ash and eventually showed his development when he bested Gary.
Pokémon's Blue and Gary: Same Person, Two Different lives
The reason Gary had to live a different life from Blue was not only to separate the two but also to balance his strength with Ash's. As the anime had no plans to let Ash become a champion anytime soon back then, having Gary succeed where Ash fails takes away from Ash's character. Since Gary had little success in the league tournaments, making him a Gym Leader would also make no sense for his character. The reason Gary becomes a professor is partially to do with this and partly because the series wanted to include other rivals for Ash. Blue, on the other hand, got to remain powerful, as well as being one of the least annoying rivals in Pokémon, as the protagonists in the games are held to a much higher power level.
Gary and Blue were almost certainly designed to be the same person; however, as the game and anime had to develop separately, so did their characters. Gary was at the mercy of Ash's slow development, and while he could be stronger than Ash, he could not be on the same level as Blue. In contrast, Blue could be a super strong trainer that encourages the player to continue to grow and provide a fun challenge. Both characters did succeed in becoming popular fan-favorite characters, so the differences Pokémon's Gary and Blue ended up having were not counterproductive to their success.