[bobdsmith]

But I don't think most atheists deny God exists.

A-theist means without theistic belief. Someone can lack theistic belief without actually making any positive claim. I lack a belief in Santa, although I don't make the positive claim that Santa doesn't exist (I would have to be omniscient to do that).

[ThePythonicCow]

But I don't think most atheists deny God exists.

I believe that the primary definition of atheism is a doctrine that denies the existance of God or any other deity.

• Atheists assert there is no God.
• Agnostics say they don't know for sure.
• Secularists disdain such theological discussions, and focus on matters of science, government and learning in this world.

[ThePythonicCow]

Well, actually, you are right in the origins of the word 'atheist'. Its original meaning is "lacking belief in the existence of God" (as you state). It's later meaning is "believing in the nonexistence of God."