the name is a rip-off of Square's Cash App: https://cash.app
Wallet is an actual wallet where you can put cards, coupons...
Pay is the whole system of APIs used to pay via NFC or online, authed by biometrics (Touch/FaceID). As a user you just add your credit card and it works better than contactless credit cards.
Apple Card is an Apple credit card with cashback backed by Goldman Sachs. US-only.