Apple Pay is a percentage paid by the bank, not the merchant.
In-app purchase is for an app being used to buy digital goods and services consumed in-app. The agreement for publishing apps says that you will give Apple a cut, and upfront purchase price and in-app purchases are how they collect it.
You can’t use in-app purchases to say order dinner to be delivered.
It would start slowly, with a minor value-add (e.g., making it easier to put/use CC info in the secure enclave, or whatever incremental step they choose), and an announcement that in exchange for "easing payments and making them more secure", Apple will be charging X% of transactions with their system.
On iOS, In-app-purchases (IAP) are used inside an app to purchase content. Because it's on Apple's device using Apple's SDK and APIs and hardware, Apple takes a 30% cut of the fee, so you charge $10, Apple takes $3 and gives you $7. Inside of the app, it uses Apple Pay, but because it's in the app, Apple takes 30%.
If not, what’s the difference between it and an app?