The word is correctly interpreted etymologically as athe-ism rather than a-theism - it is "without-god(s)-ism" not "without-theism". And deism is neither a sub-category of theism nor a sub-category of atheism - whichever way you look at it. Deism is the belief that there exists a creator who, having created, took no further part in the operation of the universe, doesn't do miracles and revelations and such. Theism is the belief that there exists a supernatural creator who remains both interested and active in the operation of the universe (most especially, by all accounts, what we do with our private parts but occasionally popping up here and there with a miracle or a revelation). Atheism lacks belief in either of these.
Pernickety pedanticism aside, I do think avowing atheism is to make the statement "the universe does/could work without an external/supernatural creator/sustainer" - it is not simply a passive "lack of belief" in the existence deities - it is a positive belief that the universe either does, or could, both exist and function perfectly well without one.
Naturalistic pantheism, which I sometimes lean towards, is kind of halfway between them - it says essentially (according to me at any rate) that there is "something that it is like" to be the universe - and that's what I call "God". It doesn't have to be called "God" but for me I don't see why not. "It" doesn't do miracles, didn't create the universe supernaturally, etc...so sometimes I try to call it "pandeism" but then if deism indicates a disinterested and uninvolved deity, how can we say the universe itself is uninvolved in the operation of the universe? So maybe it is just "sexed up atheism" - the universe doing what universes do...but for me, often, that seems to be "God enough".