Claude

He was never intended to be the same character. GTA2 already had the established character "Claude Speed" when III was developed. To make the character more easily identifiable with players, it was decided not to give him any name or dialogue. However, GTA:SA used III's character as a means of tying SA to the rest of the series (along with Ken Rosenburg from VC, etc). Because Catalina talks about him, there had to be a way for her to specify that character. He didn't have a name, so they just used "Claude" retroactively.

So no...when III was made, it wasn't the same character. Whether it is now (retroactively) is entirely up to R*. And they never said either way.