In the first case you'd have to start with a tiny, specialized payments market that you could then expand. The second case would be Facebook creating their own credit card system. Which they could probably do.
I'd recommend starting with a specialized payments market. That's how credit cards themselves got started. And you can't create Facebooks for the asking.
Now, the difference between Square and the CC companies is that square is really a gateway to those CC systems and not a credit provider themsleves... BUT once they have traction with POS merchants and acceptance by consumers could they start their own credit department? Sure. Would they want to? That is another debate. I'd wager it's much easier and still very profitable to be a gateway taking a small slice off each transaction than it is to be the credit provider.