Apple Pay and Apple Wallet have distinct functionalities, even though the two names are often used interchangeably. Apple Wallet is an iPhone app (with a companion tool for Apple Watch) that acts a digital wallet to store digital versions of debit and credit cards, auto insurance cards, boarding passes, IDs and more. Apple Pay, on the other hand, is Apple's digital payment service that lets you use your cards to make purchases at a physical location or online.
For Apple Pay in-store, you tap your iPhone on an NFC terminal and press the Side button twice. Your iPhone will then confirm it's you with Face/Touch ID or your PIN to complete a purchase. Online Apple Pay usage is similar to services like PayPal, where you choose a card and authenticate. Regardless of what you buy or where, you're using Apple Pay to purchase something with a card stored in your Apple Wallet.
Wallet can also hold plenty of items not directly tied to payments, like concert tickets or store loyalty cards. In this case, it acts as a secure place to hold these items and keep them easily accessible.