Distinquising between a Mifare DesFire and Ultralight and working with Oyster C.

Hello,

I am playing around with my arduino and the nfc shield from adafruit and ran into an interesting problem.

Whenever I try and read (wit readMifare example) my Oyster Card (London, UK Transport Card) it says that it is a Mifare Ultralight Card, however I know that it is a Mifare DesFire Card.

How can I distinquish between those two? I also get the same thing with one of my bankcards.

Thank you very much.

PS: Do most bankcards use the Mifare Classic?