"Settling With Power" is the same thing as "Vortex Ring State."
In the U.S.--where the term Settling With Power appears to have originated--it means the main rotor is in athe Vortex Ring State. It describes what happens to the aircraft when it enters MR VRS: despite having plenty of engine power available, the helicopter makes an uncommanded descent, or "settles." In fully developed MR VRS, the available engine power is typically useless to stop the descent. (FAA-H-8083-2121A, p11-9)
This distinguishes the emergency from a similar uncommanded descent that occurs when there is not enough engine power available to keep the rotors turning. This state could correctly be called "Settling Due To Insufficient Power," but is instead known as Overpitching. In this case, as well, there is a difference in terminology for the same phenomenon. In the U.S., overpitching is known as Low Rotor RPM. (FAA-H-8083-2121A, p11-15)
In both cases, European terminology describes causes, while the U.S. terminology describes symptoms...but they refer to the same phenomena.
Cause: (Main Rotor) VRS Symptom
Symptom: Settling With Power
Cause: Overpitching (of the rotor blades, i.e. raising too much collective with not enough engine power available) Symptom
Symptom: Low Rotor RPM
It seems there's one more point of confusion, however. In Canada, the term Settling With Power has also come into use, but to mean something like hitting the brakes too late. When a pilot begins to decelerate too late during their approach, reaches the limits of their engine power available given the conditions, and cannot bring the helicopter to a stop, i.e. zero groundspeed, without an overtorque, and the result is either a hard landing or a go-around.
The real problem is a lack of standardized terminology across the industry.