Not like PayPal at all - let me try to explain it in a sort of overview form. Basically what happens when you add a card is that Apple puts your device in contact with your bank and your bank generates a token (essentially a throwaway card number that is unique to your device). So, if your card was 1234 5678 9012 3456, your Apple Pay number on your phone may be 9876 5432 1012 3456 and on your watch may be 4321 0987 6556 0123 even though they all point to the same account. When you pay in person, in an app, or on the web with that device, the tokenized number is passed through the merchant and when it hits your bank, points back to your account.
In the case of a data breach or other fraud, the merchant only has the token number from your device, so your bank can issue a new one and the number on your physical card is not seen.
If you delete your card from your device, the token is destroyed, and if you re-add it, you'll get a different token number.
Android Pay uses tokenization, and I think Samsung Pay should, too, but I think those allow you to add unsupported cards as a copy. I think for this, Apple saw it as a better solution to work with banks to come on board, rather than allowing people to add cards without tokenization and the extra security benefits.
In the U.S., there's a lot of smaller banks and credit unions that have been late to the Apple Pay party, but are getting added. I suspect Apple will be working with more as time goes on (at launch, only the largest banks were part of Apple Pay and only 3 of the 4 major credit card types were supported).