The types of USB refers to the physical shape of the plug
The classic USB plug that we are all familiar with, the Type-A USB is the larger standard rectangular plug. Whilst it’s gone through a number of changes to accommodate different versions of USB, the design of the plug remains the same, which means that all Type-A plugs and sockets are compatible no matter what version they are.
Usually the other end of a USB cable uses a Type-B connector. The Type-B plug is the tall plug with the slanted top corners. Variations on Type-B have been widely adopted due to the sheer necessity of having smaller plugs at the client device end.
The mini USB and micro USB are also variations of Type-B.
The headline feature of the USB-C is that it's reversible. It's designed to be small enough to not need any mini or micro variants. The intention is that it will completely replace all types of USB on both host and client devices.