Settling with Power, Power Settling, and Vortex Ring State
This answer is from the basis of being trained to fly helicopters by the US Navy, about 35 years ago, and spending a few decades as a helicopter pilot.
The usage has changed over the years. The point @Simon made about people not using standard terms doesn't help. In American circles, an original distinction between the two terms, even when both had the word "power" in them, is that each addressed a two different case of
"I am descending"
with the phrase difference indicating
"why I am descending"
usually applied to a case where I try to stop the descent and it doesn't stop. (Clear as mud, I know ... try having your check ride grade influenced by knowing the difference :p )
Power Settling meant -- "I am out of power, and thus I am descending (and RPM is drooping)" That term is now taught as power required exceeds power available.
Settling With Power meant -- "I have more power available, but I am still descending even if I add that power." This is the case of Vortex Ring State, and that is the term now used and taught in the Navy (reference is the same link as above).
As @Simon points out, the gotcha in VRS that makes it lethal is that adding power makes it worse. The corrective action is to reduce collective pitch and fly out of it.
When the Navy taught me how to fly helicopters (81/82) our text book term "power settling" for the situation where we ran out of power and our rotor RPM began to droop, and "Settling with Power" to describe the effects of Vortex Ring state.
- Vortex Ring State
This was faithfully and well described by @Simon. Between the time I earned my wings and ten years later, when I was instructing in Seahawks, the Navy changed to use the far more accurate usage: VRS. It was interesting to see the transition and how people got used to the new term. The manuals I just checked out for V-22 and MH-60R also use that term.
So what is Settling with Power?
It's a confusing term, at best.
The continued use of "settling with power" is likely to do with where one learned how to fly, what country you are in, who your teacher was, and for how long someone used a term and may not want to change terminology.
Settling with power as a substitute for "power required excedes power available" is not universally accepted, although it appears to be a common usage in Canada. To support that point, I offer you:
Exhibit A
Exhibit B
Unfortunately, the ad hoc definition of "settling with power" as a purely power phenomena is not correct, in Canada or elsewhere. The idea that such a definition is needed for "an approach where insufficient power is available" is right on, but settling with power is not the term.
Check here: http://www.dynamicflight.com/aerodyn...ettling_power/
{snip} Evidence of the confusion caused by misuse of the terms is shown by the confusion about recirculation, which is the cause of VRS/Power settling/settling with power. It is the recirculation of the downwash that causes all the misery of VRS.
We should actually agree on a term for the falling through on an approach that is caused by insufficient power, and stick to it. ~ Nick Lappos
As regards expert advice, Nick Lappos is a well regarded helicopter aviation professional with over 4 decades of experience in the industry, and knows flying, test flying, rotary wing design, and much else. You can look him up. I find his take on most helicopter flying issues well grounded. (OK, lousy pun...).