24 VAC might be used too. In the US, control is usually 120 VAC. PLC applications would use 24 VDC.
In the motor starter, there is usually a transformer that is multi-tapped for 440, 460, 208, 240 or just twp that creates a little bit of 120 VAC for control.
24 VAC is used exclusively for air conditioners. At least that was the old way. 16 VAC fir door bells.
Power limited or class II wiring is often used so you don't have to use conduit.
We don;t know what part of the world your in.
There are "contactors" and "motor starters". 3 phase would usually have a motor starter. 3 phase protection is often employed if for some reason the system looses a phase. protection might cost an additional $100.00 USD. I used stuff from Symcomm and was very happy with it.
When you have a bulding wide single phase failure, you react. There were 36 heat pump motors, but they were affected minimalyy. there was a $5,000 cryogenic compressor and a >$5,000 USD roots blower that got protection. We used the thermal on the roots blower.