In the most general sense, both types of apps are for "payments", but Bitcoin has unique properties that could allow for applications that are impossible with the above listed examples (because of central oversight, fees, limits, etc.)
I agree that there are advantages to Bitcoin over other payment methods. No dispute there.
But your original contention was that Apple want to be able to take a 30% slice of transactions, and they can't do that with Bitcoin so they're banning wallet apps. My gut instinct says that's not the reason but I'm trying to find out more info before deciding.
Apple don't take a cut of any of the transactions done through the PayPal app etc. so I think it's safe to assume that they wouldn't want a cut of similar transactions done over Bitcoin.
So again, I'm probably missing something obvious, but I can't think of any: what are some examples of transactions that are only possible with Bitcoin where Apple would want to take a cut.
