CB in France, Bancontact in Belgium, iDEAL in the Netherlands.

Those are all nationwide networks that allow online payments (online in this case, but they also handle most non-cash payments offline) inside these countries. I think most countries have such a network (under various legal forms, for example CB is a consortium but Bancontact is for-profit, while I think Interac in Canada is a non-profit, etc) but the US doesn't have an equivalent as far as I know.