I remember a little adjustment slider to help the joystick center near 0,0

One is basically a self centring sprung up/off/down switch. That would be similar to a car indicator stalk and simple left/right arrow keys.

Another would be rotary with a stop but it sent a physical position, presumably it was something like a variable resistor or very fine resolution rotary switch. With these you could instantly position your character by the position on the ring/slider. This could be interpreted as position 1, 2, 3 etc etc.

The third was a free spinning which moved the character faster the faster you spun it. This would be how I remember Tempest playing, you could slowly nudge it or just do a fast spin & stop to quickly move around. This would produce a signal such as clockwise+very slow or anti-clockwise+very fast.