Your virtual card number
The Apple Card also includes a separate number for instances in which you can't use Apple Pay or swipe a credit card and must provide a credit card number.
This number can be found by launching the Wallet app, tapping your Apple Card, and pressing the three dots in the top right corner of the screen. Then press the "Card Information" option located below the "Payments" section and authenticate using Face ID, Touch ID, or your passcode. You should see a card number below your name.
Your physical card number
If you have a titanium physical Apple Card, that card will have its own number too —although there are no numbers printed on the actual card itself. The number is used to process a purchase when you swipe your physical card or insert its chip.
When you look at your recent transactions in the Wallet app, you'll see whether you used Apple Pay or your card number to make a payment. The last four digits of your card number for each transaction are also visible by tapping a transaction from the list and then pressing the arrow to reveal more information about it. You'll notice that those last four digits are different if you've used your physical card, virtual card number, or Apple Pay.