For the most part they would be one and the same, but I think it has to be more of a virtual inheritance if anything. That is, it has to be up to the character to implement, because:
1. There may be 2 characters of the same class. They shouldn't share a skillset (usually).
2. The character may change classes. While you may have it belong to a certain class, they should still be accessible if you change back.

Ah, that gives me an idea. Skillsets that follow the character; accessibility that follows the class (and again, they are the same in games with characters that have one unchanging class and no 2 characters with the same class... which would be by definition, of course).