Some of these terms are fluid. “Atheist” (literally meaning “without God”) is sometimes cast as a negative position (the denial of theism), sometimes as a positive position (a form of naturalism – an affirmation that only “this world” exists). It can have a practical or ideational role: so, someone might profess to believe in God and yet they are functional atheists for they act as though there is no God. Paradoxically, someone might also be an atheist in terms of profession and yet live a life that is so in accord with theistic values that the person might be something like a practical theist. Notice the way contemporaries are prepared to mix terms together, sometimes that seem quite odd such as Richard Dawkins describing himself as a Cultural Christian.
And there are self-described atheistic Christians (e.g. Gordon Kaufman; and Paul Tillich was at least a non-theist).
There is an interesting distinction that might be made without being pedantic between “atheist” and “non-theist.” The latter is not (necessarily) one who explicitly denies the existence of God (or denies theism). A non-theist (like a non-Hegelian) may simply have never contemplated theism (or Hegel). “Atheist” suggests a person has at least given theism some thought and rejected it – or not accepted it as true or probably true. Although the difference may not be obvious, there is a difference between not believing x (i.e. not believing there is a God) and believing not-x (i.e. believing there is not a God).