Much may be folded into "belief in," as you say, but that's my point. That notion is confusing and insidious in the religious context, and it's liable to lead to equivocation.
The distinction is between "belief in" as an emotion or attitude of trust, and "belief that" as an affirmation of a proposition, such as the one about God's existence. Trusting in God presupposes theism, whereas the question of atheism, about whether God exists at all is prior and more neutral. The fact that the ordinary talk of "belief in God"-- including Peterson's discourse--can mix all of this up and freely equivocate has no bearing on whether the logical distinction is sound, which it is.
You introduce another matter when you contrast belief with knowledge, and atheism with agnosticism. An agnostic would be a soft or weak atheist in that she'd lack theistic belief, just as she'd lack the belief that unicorns exist. That lack of belief is consistent with assuming it's possible such things exist after all. She suspends final judgment because the possibilities may shake out differently in the end.
But I talk more about agnosticism in this article:
