No they aren't the same. BPay is owned by the major banks, PostBillPay is owned by Australia Post.
Not sure if your card issuer treats them the same. Have you thought about getting a card that doesn't have that restriction (IIRC only Westpac cards don't earn points with BPay).
From just $6 we'll remove all advertisements so that you can enjoy a cleaner and uninterupted viewing experience.And you'll be supporting us so that we can continue to provide this valuable resource :)