Diesel Clay - PayPal pays you into a PayPal account you either set up, or link to your existing account. The account is accessed via a PayPal Mastercard (I think it's Mastercard) debit card. You take a customers payment, PayPal takes out their share and places the rest in your account. PayPal claims this to be faster access, as swiped transactions are almost immediately transferred. If you are cash or credit card poor, and away from home, having this access for expenses could be a good thing obviously.
With Square it goes to a bank account I have specifically set up to receive the payments. A friend had an issue with one of the payment systems tying up their funds due to a customer backcharge, which froze their bank account somehow, so i didn't want to get into that kind of position if it could be avoided. That is why I set up a specific account for Square payments. My experience has been from a weekend show, the funds appear in my bank by Monday afternoon or Tuesday.
Brian Reed - I am not sure it is legal to refuse to accept cash in the USA. It is the legal tender of the land. My workaround involves pricing to always come out in even dollars. If your price points match up in $20 increments, you stand a better chance with change, as the $20 is the predominant "coin of the realm" at ATMs. It may also be the predominant favorite of counterfeiters too, unfortunately.