Costume: an entire ensemble including acessories for a specific purpose, e.g. wedding costume, court costume, halloween costume, ballet costume etc.
Cosplay: costumed-play. It was coined to describe what sci-fi fans were doing at US conventions, but the term came into use at US conventions with the rise of interest in J-culture.
If you are in costume at a convention and acting the part of the character, you are cosplaying! Doesn’t matter the genre, or your perceived level of quality or how seriously you take it.
Costuming is the stuff you do in the workroom, or lounge, or in the hotel room the night before because you haven’t finished before leaving. It is the act of making, not the wearing.
No one knows if you made the costume or not when you are at a convention. Some people make the assumpton they are all bought, some that they are all hand made.
Costume also does not denote the level of quailty. In terms of grammar it is a noun or a verb, therefore neutral until you add in a qualifier (adjectives and adverbs).
I have been a student of costume since 1989. I had Waugh and Arnold memorised by 1995 and read transcriptions of 16thC texts in languages I did not know until I started that research (I am stalling at reading scans of hand written work, but I can read scanned of printed work). I am biased in that I really am a both a theoretical and hands on costumer. I also happen to cosplay.
I am primarily a costumer as I spend more time making or talking about the making than I do dressing in my work and posing or performing. But when I do, I don’t mind people calling it cosplay.