Some things that we know for sure (if my memory serves me right), though: Ranma is never seen breaking bricks in the same manner as Akane, Akane's never shown to meditate like Ranma does every now and again, and Ranma once (during the rhythmic gymnastic story) said that the Saotome school specialized in mid-air combat.
Yeah, "mid-air combat" is something we definitely NEVER see even the slightest hint about from Akane.
All that's not irrefutable proof by any means, but it tips the scales toward the likelihood of the schools being different, even if not fundamentally.
Yup, common ancestry and close enough to probably work as complementary sides of a whole, but not same.
Also, one very simple and blatant indication, Ranma and Akane are supposed to marry to "unite the schools". That would be completely irrelevant if they practised the exact same thing.
Although my memory's not perfect, there were two grappling moves in the dogi story alone that I don't recall Ranma ever doing. (I'm sure he could do them if he wanted to, but that's an entirely different argument.) If that turns out to be true, it stands to reason that it suggests that her style might be different, if we assume it was Akane and not the dogi doing it.
Yes. And while especially drawn martial arts is difficult to see as it's supposed to be for real, it's definitely possible to find more examples of how they're drawn with their own distinct styles. Akane does things one way, Ranma do them in another, they overlap, but not enough to be the same.