To make it all clear:
Red is the main character of the games Pokémon Red/Blue/Green/Yellow. There is a female protagonist in FireRed/Leafgreen, but is probably not canon, as she has never appeared in future mainline games, or mentioned about by NPCs. She does appear in Coliseum, XD, and Battle Revolution games, but those are not canon.
Ash is anime adaptation of Red. Technically, Red and Ash ARE the same person, as Ash is based on Red. However, other than having the same clothes, and both having Pikachu and the Kanto starters, they are NOT the same characters.
This is like the original source material vs Hollywood adaptations. Take manga or anime Goku vs the 2009(?) DBZ movie Goku example. They both wear the same clothes. They both have weird spiky hair. They both meet alot of same cast of characters, they both had their grandfathers die, and both can do the Kamehameha. Now, despite these two sounding and looking the same, are they the SAME character? Nope! One is a character that fans love and can instantly remember. The other is a... What the flippity heck is this? Goku's not a white guy!! When he first saw Master Roshi use the Kamehameha, Goku INSTANTLY mastered it without training, AND he even had an even giant blast than Roshi's! What about movie Goku? He learns it by practicing making farts with his hand? And even then, when he finally does it on Piccolo, he has to do some complicated bending technique??!! Where's the flying Nimbus and his staff?
I don't get why there are people who still think they are the same characters. I get if you're a kid who's trying to understand some things. But if you're an adult, you should be able to understand that adaptations will never be perfect. Unless you plan to make it a full on word-for-word, scene-to-scene adaptation, you have to tell your own stories to differ from the original. This always causes slight changes on the source material, whether it be the scenarios that happen, the motives and goals and personalities of the characters, the setting, etc.