As gmood suggested, the PayPal card is issued and handled by Synchrony - it's a cobranded PayPal card. Just like getting the Marvel card doesn't mean your account issued by Marvel directly, so does this mean your PayPal card isn't issued by PayPal.
It's pretty simple really. The business debit used to require either a premier or business PayPal acct, but the premier and basic have since been merged so anyone can get the business debit, just go to PayPals site, find it, and apply. As long as you have a PayPal account you'll be fine...actually based on your last post it sounds like you may not have a PayPal account or want one? It's actually required for either of those products - but you shouldn't keep any money in the account for this to work anyway.
There's a thread here that details the setup:
http://ficoforums.myfico.com/t5/Credit-Cards/Earn-3-on-everything-using-one-card-LONG-UPDATE/td-p/51...Essentially you get the debit card and the CC, and when you go to the debit card account webpage on your PayPal acct you set up the PayPal cash back cc as the backup funding source (can only do it with a PayPal cc which is why you can't just do it with the Citi DC). The debit card pulls from the PayPal account balance, but when it's $0 it reverts to the backup funding. Then you'll get 2% on every purchase with the debit card via the credit card - each transaction goes through both - and 1% for every credit transaction on the debit card (when ran as debit theres no extra 1% but you still get the 2% from the CC), the main stipulation being to get the 1% from the debit card you have to run $100 through it in that given month.
So basically after you set up the backup funding (takes like 2 minutes if that), you just sock drawer the credit card and carry around and use the debit card, ensure that your PayPal account is always at $0 when you use the card (the cash back deposits into the PayPal acct so transfer it out to your checking acct each month), and yeah just ensure you put $100 at least through it to get the 3% instead of 2%. Also note there are certain purchases that don't take credit, or like charitable donations where it's better not to use credit - 2% on debit transactions is friggin stellar in today's market. Of course even if you don't hit $100 you'll still get 2% on debit transactions as well as credit transactions.