In 2007, there weren't any other accelerators, at least that I was aware of. We were almost the prototypical Y Combinator founders: We were highly technical but had never done a startup before. We also didn't know anyone in the Valley - investors, other entrepreneurs, potential hires. YC seemed like a great way to bootstrap that network.
Square is turning informal, cash transactions, like you would do with a taco truck, into card swipes. Stripe is more for the Internet, it's focused on the kinds of transactions that weren't possible years ago. We think about how you would buy things from a mobile phone, crowd-funding, how should that work.