Prefixes, Unofficial Words, Clarifications

a-
var. of an-
1 before a consonant, meaning “not,” “without”

As in "atheist."

non-
a prefix meaning “not,” freely used as an English formative, usually with a simple negative force as implying mere negation or absence of something (rather than the opposite or reverse of it, as often expressed by un-

Dictionary.com provided no definition for "nontheist." Guess it isn't an official word so I Googled it. I was directed to Wikipedia:

Nontheism is a term that covers a range of both religious and nonreligious attitudes characterized by the absence of — or the rejection of - theism or any belief in a personal god or gods.

So what I believe is Not Theism under the umbrella of The Absence of Theism.
Glad I cleared that up.