The following diagram shows the main types of charging connectors. Both Level 1 connectors and the NEMA 14-50 connector (2nd Level 2 connector) are standard household US line power plugs. The other Level 2 connectors are the J1772 which is a universal connector that all EVs can use (Teslas come with the necessary adapter), and the Tesla connector.
Almost all EVs come with one of the three Level 3 connectors. The CHAdeMO connector is only used by the Nissan Leaf while the CCS connector is used by all other EV makes, and Nissan have announced a future SUV model that will use the CCS connector. Newer Teslas in Europe use the European CCS connector, and Tesla have announced that they will open up the Tesla Supercharger network to other EVs via an adapter, so universal compatibility seems the likely future state.