You're pretty much positing the analytic-synthetic distinction, dude.
The truth of a claim is necessary because of its correspondence to reality, not because of the meaning of the terms. Consider that we could simply be mistaken categorically about number terms. For some reason, when we add 1 and 1 we always get 3. We would come to think, that's the order of things.
Patently absurd with such elementary arithmetic, but some higher maths posit things that can be absolutely, deductively valid but we realize "Oh wait, we didn't compute the constituents right.".
That's the real distinction you're looking for, though: 1 + 1 = 2 is deductive. It is, however, not more true or more obviously necessary, even if we perceive it to be that way.