Nontheist is defined as covering a wide range of people, all characterized by lacking belief in any gods, rejecting of belief in gods, or deny the existence of any gods. The definition of nontheist is effectively the same as the definition of atheist — the prefixes "a-" and "non-" mean exactly the same thing. The label nontheist was created and continues to be used in order to avoid the negative baggage the comes with the label atheist due to the bigotry of so many Christians towards atheists.
The Oxford English Dictionary defines non-theist as "A person who is not a theist." This is the same as the broad, general definition of atheist, thus the two labels can be used interchangeably.
"Mr. [Charles] Southwell has taken an objection to the term Atheism. We are glad he has. We have disused it a long time [...]. We disuse it, because Atheist is a worn-out word. Both the ancients and the moderns have understood by it one without God, and also without morality. Thus the term connotes more than any well-informed and earnest person accepting it ever included in it; that is, the word carries with it associations of immorality, which have been repudiated by the Atheist as seriously as by the Christian. Non-theism is a term less open to the same misunderstanding, as it implies the simple non-acceptance of the Theist's explanation of the origin and government of the world."
- George Holyoake, "The Reasoner," 1852
"The difference between theism and nontheism is not whether one does or does not believe in God.[...] Theism is a deep-seated conviction that there's some hand to hold [...] Non-theism is relaxing with the ambiguity and uncertainty of the present moment without reaching for anything to protect ourselves [...] Nontheism is finally realizing there is no babysitter you can count on."
- Pema Chödrön, When Things Fall Apart