Add Discover and you essentially have a complete list of credit networks in the US. The other offerings you see are mostly white label products built on top of the usual credit networks.

I wouldn't consider PayPal a competitor since they don't operate a credit network (although they sometimes facilitate money transfers that don't involve the credit networks). Whenever a physical credit card is used in the US, it's almost always the case that one of those four credit networks collects an interchange fee.