USB-C is a connector. Part of the confusion is that USB specification versions have come to be associated with the protocols and speeds defined there. The basic division is between USB2 and USB3 which are separate protocols on different wires. USB-C has multiple high speed lanes.

USB 3.0 defined the SuperSpeed protocol and 5GBps speed. Later versions increased speeds, 10GBps (USB3.1), 20GBps (USB3.2). These were also called Gen1, Gen2, or now just the speeds.

Then, there are alternate modes which run other protocols over high speed lanes. DisplayPort is the most common one.

Next, USB4 defined USB4 protocol which multiplexes SuperSpeed and DisplayPort over two high speed lanes. USB4 requires USB-C. This is basically Thunderbolt standardized. Specification also defines 20Gbps, 40Gbps, and 80Gbps speeds.