In almost all microwaves, the control circuitry or mechanical switches only ever switch 2-3 power circuits: motor+fan(+bulb sometimes separately) and the heating (transformer+diode+capacitor+magnetron) high voltage circuit. It can therefore only switch the heat between 0 and max, usually in a slow (15-30s period) PWM cycle (that hopefully does not coincide with the tray rotation period). The inputs can be manual only, or sometimes there is also a scale, moisture sensor and microphone, along with thermal fuses for safety.

I think the pizza setting is just generic medium one with short 50% cycles to allow the heat to spread. The popcorn setting can be much more interesting:
https://www.youtube.com/watch?v=Limpr1L8Pss