[wan23]

You can Appple Pay with the Apple Cash in your Apple Wallet. You can also pay off your Apple Card balance with the Apple Cash, and also using the Apple Card earns you Apple Cash back. It's not a card in the wallet, but because the wallet UI only shows card UI components it's not surprising that you thought of it that way.

[WorldMaker]

Apple Cash shows up as its own card in the Apple Wallet. It's the bank account Debit Card pairing to the Apple Card credit card if you have both. You can have an Apple Cash card without having an Apple Card, though with the "Daily Cash" that Apple Card earns you currently can't have an Apple Card without an Apple Cash card (so far as I'm aware).

(Some confusion here is that you can have a separate Apple Store/iTunes credit that isn't Apple Cash and doesn't show up as a card in the Apple Wallet and can only be spent in the Apple Store/iTunes. Given the nature of how gift cards work that's likely to remain a separate "cash fund" and the two separate balances may always be a little confusing, with some people likely putting money into one when they meant to put it into the other. Hopefully Apple may find a good way to communicate the differences between them.)