You are describing two degrees of the same thing here
Wrong. It is quite certainly true that rocks and weeds don't believe god exists. It is just as certainly true that they can't believe god doesn't exit. Proper negation is
essential. It can be said of anything incapable of belief that, for any claim X, that thing doesn't believe X (this includes statements like "crows are black" and "crows aren't black", because a rock doesn't believe either statement is true, while it is impossible for anybody to logically believe that one statement is true but believe the other isn't).
So the conversational implicature then is that an agnostic is really just a wimpy atheist.
Time was, physics didn't have "interpretations". There were not families of interpretations for Newtonian mechanics, electromagnetism, etc. There are, however, families of interpretations of quantum mechanics. Most physicists would agree that they don't believe gravitation to exist. Few would say they believe gravitation doesn't exist (gravity is perhaps
the unsolved problem of modern physics).
In conversation, we frequently say things like "I believe he's at home", "I believe Kepler's laws were proved by Newton", "I don't believe that's the day", or "I believe it's happening tomorrow". Such mental state predicates belong to the (linguistic) realm of epistemic modality: they express our degrees of certainty, much like "I don't think Kepler's laws were proved until Newton" or "I guess he might be at home." They are important for discourse
precisely (albeit not solely) because they allow us to distinguish between not believing and believing not. That is, they allow us to express our views in terms of doubt rather than negation.