How many kinds of USB-C to USB-C cables are there?

Classic USB from the 1.1, 2.0, to 3.0 generations using USB-A and USB-B connectors have a really nice property in that cables were directional and plugs and receptacles were physically distinct to specify a different capability. A USB 3.0 capable USB-B plug was physically larger than a 2.0 plug and would not fit into a USB 2.0-only receptacle. For the end user, this meant that as long as they have a cable that would physically connect to both the host and the device, the system would function properly, as there is only ever one kind of cable that goes from one A plug to a particular flavor of B plug. Does the same hold for USB-C? We all know the answer to this mess.