The terms 'vortex ring'(European) and 'settling with power'(US) are definitions for the same situation, i.e significant vertical descent (>500fpm) with power applied(>50%tq) at low airspeed(<30ktas).
Having taught in the US and UK I found i could use the term settling with power effectively when descibing how to recognise the early stages of the effect in order to not let it manifest into the full and irrecoverable condition. Incipient vortex ring state as a term falls a little short for me and I save that for the full monty.
Power settling once again is a US term that is sometimes used to descibe limited power operations, i.e that point during the approach when a max power limit is reached and technique takes over as the means to arrive safely.
It can be confusing and I dont tend to use it, after all limited power is precisely that, limited power.