It appears we have a definitions disparity.
I usually operated under
Theist. One that believes in some form of deity, or world view handed down (Buddhism would probably count under this, as would many tribal religions) based on believing something rather than theoretically being able to prove it/demonstrate it.
Agnostic. Undecided on the matter but not necessarily a theist. Arguably the wishy washy approach.
Atheist. One that would hold gods as most cultures, religions, creation stories... would define them to not describe
Anti theist. Much like anti other things would be one opposed to theism as a concept, and would probably argue against its use in government and such like. Or if you prefer "believe what you want to believe, I don't" vs "I don't believe and it is a silly idea, I want it out of any thing that can trouble me". It would be entirely possible for an atheist to have a position on religion's role within the government and similar type things and it might even be "no way, no how" without going into anti territory too. Major overlap with the concept of militant atheist, though we can probably have another debate as to what that means (who made it, does anybody choose to identify as it rather than being labelled...).
Broadly speaking all anti theists are atheists but not all atheists would be anti theists, I am not sure if any atheists would find anti theism as a concept to be objectionable . I imagine there are ways to blur lines (I guess you could follow a strictly interpreted version of Buddhism, as opposed to a more literal one if I may confuse religion study terms) but as a broad concept go with that. You can be a theist and strongly disagree with another religion, or another interpretation of your religion, but it is not the same concept. You could also argue for some of the same things (no religion in schools/government say) whilst being a theist quite happily, it might be against interests of the religion (or it might not, if you don't grow up one it is easier to get you to another perhaps) if numbers and funds are a concern but that is a different matter.