The debit card lets you spend your PayPal balance directly, or withdraw it as cash from an ATM. There are no fees other than ATM charges ($1.00 plus the ATM's fee), and if you spend more than you have in PayPal, the rest will come from your checking account or credit card.
The PayPal branded prepaid card has no relationship to your PayPal account, at least until you link the two yourself later, which adds some extra features. It is backed by an account at a separate bank and works most like the prepaid cards you can get from Walmart or Green Dot... including the $4.95 monthly fee.
If you already have a bank account, the PayPal debit card will be just fine, but you would really only need it if you regularly get income though PayPal and want to spend it in a hurry instead of waiting to download it to your bank account. (I have one.)