

Theism is the belief in a god or gods.
Atheism is the lack of that belief. You can be an atheist and simply lack belief, or you can affirmatively claim that no gods exist.
Many atheists are somewhat in the middle: for example, there are certain god claims that are so patently ridiculous (e.g. Xenu) that I do claim that they don’t exist, whereas there are others that are probably unfalsifiable (e.g. a deistic god) and so I don’t think it’s possible to make a legitimate claim that they don’t exist.
Agnosticism deals with knowledge, not belief. It’s right there in the word: “gnostos” is the Greek word for knowledge.
I understand where you’re coming from and I probably wouldn’t have worded things in the same way the person you’re replying to is, but there are a lot of misconceptions out there around what atheism is. For example I’ve talked to people who exit Christianity and simultaneously call themselves atheists while developing a belief in a different god, and this is objectively not atheism. Similarly, there’s often an atheism vs. agnosticism confusion which I addressed in a different comment here.