^ It is complicated indeed. So from what I gather:
Socially and culturally, you would refer to people as "Turkish".
Language-wise, you would say "Turkic", as in the "Turkic language family."
The emergence of the word "Turk" is a political denotation. As in folks who are from the nation of Turkey.
Hmm. This gets confusing pretty quickly. For the most part, my references are usually cultural/social, so I think I might be safe if I just use "Turkish" all the time, until someone corrects me.