the monotheist believes in the concept of a god ... The atheist doesn't believe in the concept of a god at all.

That's a fallacy. For instance I could believe in the concept of Zeus, the Greek God. But that doesn't mean I do believe in the existence of Zeus himself.

Or in a more modern vein: I do believe in the concept that there are other worlds in the Universe with intelligent life who can travel in spaceships. But I certainly don't believe that UFOs that visit Earth exist. And I never will, unless there is incontrovertible proof that one that visits us exists. That's not a contradiction, I just think that there are uncrossable gulfs of time and distance that keep the rare, few and far between, intelligences apart. After all, it's only a few hundred years since the Atlantic kept the Europeans and the Aztecs apart, such that the Europeans with their white skin were considered to be unknown Gods by the Aztecs when first seen by the Aztecs.

You can be sure I had a moment of panic on seeing your reply that I had written 'believes' instead of 'disbelieves', but no, on checking, I saw that I had really written 'disbelieves' after all. :)

the monotheist believes [ .. } the others that people worship are false gods.

The atheist believes that all the Gods that people worship are false gods.