Gods,” I think you’re talking about what Christopher Hitchens called the “anti-theist.” Nonbelief is the same as atheism. Both words mean “without theism or without the belief that the creator God exists.”
There isn’t really any adult nonbeliever in the neutral sense you’re going for, as in someone who lacks a theistic religion without actively rejecting any, because this person lives under a rock and isn’t aware that religions exist. If you’re aware that religions exist and you lack belief in them, you’re an atheist even if you haven’t spent much time delving into the reasons for your rejection of theism. If you don’t make it your life’s mission to oppose religion, though, you might not be an anti-theist or a “militant atheist.”
The question of the burden of proof in these debates is somewhat controversial, but I agree that the theist has a heavier burden of proof than the atheist or nonbeliever.
As I point out in this article, though, and as has rankled some other atheistic readers, “atheism” can readily be distinguished from “the atheist.” Atheism may be just a negative viewpoint that doesn’t have to be supported with a separate burden of proof. But atheists are people who have positive worldviews (including, for many, secular humanism, philosophical naturalism, neoliberalism or some other politics), and those worldviews do carry a burden of proof.
In this article, I criticize atheism in the larger sense, in so far as atheism is part of many atheists’ positive worldview. See, for example, the third criticism.