IMHO, there are three things at play in these discussions.
1) People having different experiences and frames of reference.
Personally, I distinguish normal movement from IP/IS and within IP/IS I distinguish the way of movement of the internal arts (neijia) from the non-internal arts. Which perfectly demonstrates that I can't get the terminology right even when I'm just discussing this with myself.
I mean, there are non-internal arts that do use Internal Power / Internal Strength?!
In any case, I experience a clear enough difference between these three groups to place them in a separate category. Other people with different experiences might disagree. The question then becomes: do we distinguish different categories or do we just use different names for them? That's a very difficult (if not impossible) discussion to have over the internet.
2) Everyone wants to be the most internal.
Everyone knows the internal arts are the most l33t of all martial arts. They are the most awesome, the most pure, the most ultimate. If the Five Point Palm Exploding Heart Technique would exist, it would be in one of the internal arts.
So if someone says what I do is not internal, or not fully internal, it means I am not practising the best way of movement known to man.
3) What Hunter said better than I could have.