What's the diff between physical and virtual cards?
Physical can see can touch, virtual can see cannot touch.
Kidding...
IIRC, when you sign up and go through the verification process, the virtual card (numbers) will appear in your app. If you also want the physical card (will have a different set of numbers), you've to request in the app.
For me, I added the virtual card to my TnG app (for immediate use) while waiting for the physical card to arrive. When the physical card arrived, I added that to my Apple Wallet. Thus, 2 cards to use.