The rate of turn is the amount of heading change (in degrees) per unit of time (usually seconds) => change of heading rate of the aircraft.

On the other hand, the yaw rate is the rate of rotation about the aircraft’s yaw axis. Yes, the heading will also change if you yaw the aircraft, so you can say that it is the same as the rate of turn. However, a rate of turn is not necessarily (and ideally) equal to a yaw rate as banking the aircraft for a coordinated turn (no slip and skid) will not make the aircraft rotate about its yaw axis.