"I ran my first lathe directly from the wall socket for many years."
Me, too! Bought it at 14, I'm 72 now, lathe still runs, but I don't!! If we're talking about a small motor here, and it's single-phase, many have overload thermal switches contained within their windings. These open the feed circuit if the windings get too hot. Occasionally, a switch is found used in conjunction with small motors incorporating an overload device within the switch. My experience has been to find these on very old installations of over 1 HP, but still single phase.
3-phase motor operation, at least here in the States, almost invariably uses a "motor-starter", which is a fancy name for a relay which contains an overload device capable of cutting off power to the motor itself. Such starters often incorporate lower voltage coils (operating voltage) than the motor voltage used. Some designers prefer very low control circuit voltage, 12 or 24 volts, or so. Such thinking provides safety from shock hazard to Maintenance workers, to some extent; however, since control and controlled voltages are used in common within the same service enclosures, such protection is a rather moot point to be argued among those designing the stuff. An exception is the case where machine operators and peripheral workers, loading parts perhaps into temporarily motionless machine elements, actually perform control functions at their more or less remotely-located work stations, there being switches mounted for their use. Such operation is wisely done using low voltage. Workers have a way of beating HELL out of switch stations and the like!
Personally, I prefer 120 v. controls, and use whatever the motors require, commonly 460 v. 3-phase. Note that the control voltage is universally single-phase, regardless of voltage used. jack