Define "completely different" please. The two mathematical representation of quantum mechanic were completely different until it was shown that they were equivalent..

Would it be reasonable to claim that if different mathematics give the same answer in all cases, then it is really only different forms of a single mathematic?

They could produce different answers for cases that don't occur in nature. For example you can find many polynomials that go through a given point set (all possible observations you can make) but disagree wildly outside of the point set.