The four types of focus drive Canon offers are:
1. Manual only (i.e., Tilt Shift lenses, 65mm Macro).
2. Micro motor (i.e., 50/1.8 II, many others that aren't marked USM or STM)... Least expensive, but slower, noisier, and it can be more erratic. For example, the 50/1.8 is said to be virtually impossible to Micro Focus Adjust, because it rarely refocuses exactly the same way with successive attempts. Cannot/should not manually override focus while the lens is set to autofocus. Have to turn off AF at the switch first, otherwise there's risk of damaging the lens' focus mechanism.
3. STM or Stepper Motor drive is relatively new and was developed especially with videography in mind, but certainly works fine for still photography too. Adds a little cost (approx. $50 per lens), but is a little faster and a lot smoother than micro motor. It's also very quiet. It is "focus by wire", which means that the manual focus ring will merely turn unless power is applied to the lens (half-press of the shutter release button, unless using Back Button Focusing method in which case that button must be pressed). This probably won't work in what Canon calls the Basic Exposure mode settings found on many of their cameras (the highly automated "Scene" modes: "Running Man/Sports", "Mountain/Scenic"). Camera needs to be in what Canon calls the Creative Exposure modes (Tv, Av, P, M).
4. USM or Ultrasonic Motor drive has been around for quite a while and is the fastest and most accurate/consistent. Usually the most expensive form of drive, found mostly on mid-grade to premium lenses. Not as quiet as STM, but very quiet none-the-less. In most cases it allows for what Canon calls FTM or Full Time Manual override of autofocus, meaning you can manually operate focus at any time without harm to the lens (but see Note 1 below). This is useful when refocusing, for example, and wanting to throw the lens out of focus.
Note 1: Some USM lenses use what's described as a "hybrid" form of drive. The EF 50/1.4 is one example. Some folks feel this drive system is prone to rapid wear and tear if FTM is used a lot with it.
Note 2: A few USM lenses are "focus by wire", too, but can be manually focused so long as they are mounted on a camera and the shutter release button is half-pressed. The EF 85/1.2L II is an example of this. This is same as STM lenses.
I don't use any STM lenses so really can't say about "STM-compatible" cameras.... My understanding was that STM is fully usable on all EOS for still photography, can be used to shoot video on any EOS capable of it, but had some unique advantages for videography, in particular, when used in combination with "STM-compatible" cameras. Since I don't shoot video with my DSLRs, either, I really don't know the advantages offered by using an STM lens on an STM-camera.
In cases where there are both micro motor and STM versions, the STM version of a lens is often the latest and most updated, so might also benefit from other improvements optically or functionally.