"Settling With Power" vs "Power Settling"  

A lot of this just comes down to different word choices used in different parts of the world to describe the same kind of events.  Then once you had people writting text books that would be used by different countries they started to combine things.  If you in trained in Canada vs the USA you had different terminology with settling with power vs vortex ring state, there is a great post I can try and find on PPRUNE that actually documented Army vs Navy and where the terms were actually created and why when you eventually had the FAA Rotorcraft flying handbook you have "Settling with power/ Vortex Ring State" and then goes on to describe a single event.

Ultimately you have 2 scenarios.

Scenario A - Helicopter starts a descent at speed least than ETL, descent greater than 300 feet per minute and is not in an autorotation.  Buffeting is felt, mushy controls and application of collective makes it worse.

Scenario B - Helicopter at heavy gross weight, at high DA flies a normal approach.  Allows rate of closure (combinations of speed and rate of descent) to get to high before getting the power in to start slowing down.  Aircraft is perfectly able to create lift, good clean air in the disc, but the amount of lift being created is not enough slow the rate of closure to arrive at a hover prior to the running out of space.  Power being applied is helping and aircraft is slowing down but it isnt enough to stop the momentum that you have allowed to develop and aircraft hits the ground. 

In this scenario that aircraft may very well be able to be picked up into an in ground effect hover without issues but the poorly flow approach at the limits of the performance of the aircraft allowed it to "fall through."  In the extreme version of this if you have put the aircraft past its performance ability the hitting of the ground could be much harder.  This commonly also has the pilot over pitching the aircraft in an attempt to stop from hitting the ground, engine is giving all it can to maintain RPM but then the pitch pull continues, rotor rpm drops which causes aircraft to fall faster and pilot pull harder drops RPM faster, at the same time the tail rotor RPM is of course dropping causing the nose to swing in direction of torque, pilot inputs more power pedal, greater pitch of tail rotor blades further the loss of RPM and aircraft rapidly falls to the ground. 

Scenario A is an aerodynamics problem

Scenario B is a flight performance planning problem 

Scenario A it is always accurate to use the term Vortex Ring State (VRS) though most of us in training only get into the incipient vortex ring state (IVRS) you are just touching the edge of the box, enough to know the warning signs and get out before it gets deep.  Anyone who has allowed an aircraft to go past IVRS and get into full blown VRS will tell you in is a terrifying experience.  There are stories of CH53's starting at 10,000' and almost not getting out of it and rates of descents that are in excess of 2000-3000fpm and almost full control deflections having no effect on the attitude of the aircraft.

Scenario A is also called settling with power, rotorcraft flying handbook uses the term interchangable with VRS.

Scenario B has been less officially termed but many have called it settling with insufficient power, power settling, falling through, mushing.  Also in different parts of the word they use settling with power to describe this scenario which is where most of the confusion comes from.