I agree, I can just generate and send an invoice through PayPal if needed, to accept payments that way. I also can display the payment page on-site where the client can enter their information using their own computer or internet connection. Just for security reasons or breaches that can happen I wouldn't want to swipe cards on-site, but rather have them input their information through PayPal.
Different things work for different people, SquareUp seems to be good but I don't know how secure it is as it links up credit cards, peoples information, bank account info etc etc. PayPal is its own bank account which is pretty cool. Plus you can put 'buy now' or 'pay now' customized payments with options that can be accessed from your website.