Everyone has a different concept of what every content word (noun, verb, adjective, adverb) means. That is because we learn everything by association with experiences, all of which differ. For example, a prototypical "dog" for one person might be more like a collie for one person and a terrier for another. That does not mean that we claim not to believe in the existence of dogs because we cannot all have the same set of beliefs about what is typical. Our associations overlap enough that we can generalize across them. Gods are not learned through interaction with them, but they are learned by analogy with other common experiences--authority figures such as parents and adults, strong people, smart people, good people, etc. Gods are typically conceived of as super-powerful, super-intelligent, super-good agents that respond to prayers. We pretty much interact with them in the same way that we would with other human beings. They have the highest imaginable qualities of other human beings, especially social status.
Now, it is true that many people try to abstract away from the obvious anthropomorphism we impute to gods when we first come to learn the concept. Very intelligent people have very sophisticated models for gods that are less and less humanlike. Nevertheless, it is hard to find any theist who doesn't slip back into the human-interaction mode. That is, even very sophisticated theists tend to feel reverence, loyalty, and a need to pray, as if they were interacting with an intelligent agent of some sort. I have never known a theist who could consistently avoid some amount of anthropomorphism, despite all claims to the contrary.
When I say that I am an atheist, what I mean is that I reject belief in beings that have minds that exist independently of physical brains and are capable of exercising god-like control over physical reality. I do not know for a fact that such beings do not exist, but I treat their existence with the same level of credulity that I give to other mythical beings--leprechauns, centaurs, pixies, wizards, etc. If somebody wants to argue that I cannot reject belief in gods because there might be some very special definition of a god that I am unaware of, I treat that person as someone who does not know what he or she is talking about--because that person quite literally does not.