The inverter can be made "self-protecting": It's got 'intellect' and it is able to shut-off the output. Thus no sort of external protection is necessary.
Classic motors are different: as they do not have any 'brains', there is a need to protect them in case of overload, shurt circuit etc.
In my ambient this is called a "motor protection switch" - consisting of a fast-acting 'fuse' (actually a magnetically engaged switch) in combination with a slow acting device that is normally not a bimetal element, but acting very much like a such.