@Intrepid,
I agree to a limited extent. All theists do not have the same concept of god--but they do believe that there is a god (although, see the caveat below). Some atheists simply don't believe that there is a god, while others believe that there is no god. That may seem like a distinction without a difference, but it strongly colors the responses of atheists. I would also add that not all church-going people are, apparently, theists. Ipsos in Canada and Pew Research in the United States have, in recent years, been asking people who complete their religious surveys if they believe in god. By that, i mean that they ask everyone, not just agnostics of atheists--they also ask the question of those who profess a religious affiliation. About 10% of those who profess membership in a religious sect respond that they don't believe there is a god--the so-called weak atheist position.
As with all too many aspects of human behavior, the assumptions all usually oversimplified.