1. Difference in Knowledge
   A gnostic atheist not only believes there are no gods, he also claims to know there are no gods.

An agnostic atheist doesn’t believe in gods, but doesn’t claim to know there are no gods.

2. Difference in Affirmation
   A negative atheist merely lacks a belief in gods. He is also called a weak atheist or an implicit atheist.

A positive atheist not only lacks a belief in gods, but also affirms that no gods exist. He is also called a strong atheist or an explicit atheist.

3. Difference in Scope
   A broad atheist denies the existence of all gods: Zeus, Thor, Yahweh, Shiva, and so on.

A narrow atheist denies the existence of the traditional Western omni-God who is all-good, all-knowing, and all-powerful.

4. Difference in the Assessed Rationality of Theism
   An unfriendly atheist believes no one is justified in believing that gods exist.

An indifferent atheist doesn’t have a belief on whether or not others are justified in believing that gods exist.

A friendly atheist believes that some theists are justified in believing that gods exist.

5. Difference in Openness
   A closet atheist has not yet revealed his disbelief to most people.

An open atheist has revealed his disbelief to most people.

6. Difference in Action
   A passive atheist doesn’t believe in god but doesn’t try to influence the world in favor of atheism.

An evangelical atheist tries to persuade others to give up theistic belief.

An active atheist labors on behalf of causes that specifically benefit atheists (but not necessarily just atheists). For example, he strives against discrimination toward atheists, or he strives in favor of separation of church and state.

A militant atheist uses violence to promote atheism or destroy religion. (Often, the term “militant atheist” is misapplied to non-violent evangelical atheists like Richard Dawkins. But to preserve the parallel with the “militant Christian” who bombs abortion clinics or the “militant Muslim” suicide bomber, I prefer the definition of “militant atheist” that assumes acts of violence.)

7. Difference in Religiosity
   A religious atheist practices religion but does not believe in gods.

A non-religious atheist does not practice religion.

You are confusing atheism with atheists. There is one kind of atheism. If you do not believe in the existence of any gods, you are an atheist...it is that simple. However, there are many different kinds of people, some of whom are atheists; therefore, there are many different kinds of atheists--some aggressive, some more laid back etc.

People misuse the word atheist all the time. I have seen Christians refer to other Christians as atheists simply because they don't believe exactly the same things.

When I say I'm an atheist, I mean only one thing: I do not believe in any gods. Period.
Whatever anyone else chooses to think it means is on them, not me.
I'm not going to spend much time trying to explain what is incredibly simple.