Are there RPGs where some of the character creation is partly done during play?

[Knaight]

I agree with what I think you mean, I just phrase is differently. 3.x re-defined "class" to be something that has nothing to do with class.

The term class has been used for the 3.x style and not just social-class for a very long time in RPGs. That's not to say that it isn't used for both, although generally games try to avoid using the term for both game classes and social classes in the same game too much (which is really easy for most games, as they aren't game class based anyways).