As far as I know, when you pay with a regular credit card, the data is required (and thus stored) because the vendor needs this information to receive the money from the credit institution. As you pointed out, this leads to several issues since this data can potentially be stolen (for example, through NFC skimming) or somehow obtained from the vendor/payment provider and then used with the CVV (if even needed) to make purchases.
When you pay with Apple Pay, you never provide credit card details—not even your name or address. By saving the card to your phone and unlocking the phone before use, Apple provides the vendor with a token. The vendor then exchanges this token for the corresponding amount of money with Apple, which in turn receives the funds from the credit institution.
Credit card details are usually (and by European law must be) encrypted. However, trusting a small merchant at a convention who sells you handmade art to maintain these standards is another matter.