Is everything that is logically possible also mathematically possible, and vice versa? Note, I am not suggesting that logic and mathematics are identical. I am merely asking whether logical possibility is the same thing as mathematical possibility. Even if logic and mathematics are not identical, it could be that logical possibility is coextensive with mathematical possibility.
This is very vague due to the fact that little exposition has been done on the background modality in question (the way "logical modality" behaves is not all that clear: this depends on how one demarcates the problem of logical constants and various other issues stemming back as far as Carnap, Wittgenstein & Tarski).
Similarly, not very much detail has been given on what is meant by mathematics here. If we were to hypothetically say that "mathematics" just is set theory, like ZF, formulated through interpreting a first order theory like FOL, then there will be models of FOL that are not models of ZF, so you could argue that the "logical modality" is "broader".
I'm putting scare quotes around 'broader' because, strictly speaking, the amount of possible worlds is not expressible in set theory, and so we cannot say things like "the set of logically possible worlds is larger than the set of mathematically possible worlds" (because neither of these are sets: this is well known although some outdated philosophy lags behind, see Possible Worlds & The Upper Bound Problem)