Several answers address the difference in emphasis (the emphasis on biscuits vs the emphasis on the container), I think there's an extra layer in there in that a biscuit tin would often be assumed to be more specialized or dedicated than the tin of "a tin containing biscuits"... some biscuit tins are decorated, some are collectible, some, okay most, are brand specific, and some are the tins which always contain the biscuits. A tin of biscuits might mean any tin, generic or otherwise labelled, or even a non-tin-box container if tin boxes are more common in the area or in local dialect, similar to how we might say box even for a round container of something.
I'm probably making a muddle of it, but I mean the term is a bit more specialized, a bit narrower in meaning, than "the container that holds the biscuits". I'd expect something sturdy, reusable, probably elaborate, usually round, in addition to being specifically labelled with the word biscuit or associated with a biscuit brand on hearing "biscuit tin" and that extra layer of connotation would not be there for, say, the box of a cookie box (maybe cardboard and disposable, maybe fancy wood or metal), or a tin of, say, peas (recyclable can), or even a can of biscuits if such a thing were to be found (I've seen cake-inna-can, so, shrug). That may have something to do with what is more available where I am, but it is an association that would be common in my area.
I would also be surprised to hear the phrase biscuit tin be applied to a tin box or other container that happened to contain biscuits but had another specialization or label (ie, the biscuits are in the pasta tin... not the popcorn tin, that has buttons!) unless their use for biscuits was well established and habitual, or to describe, say, a generic tin that contains buttons, as others have mentioned biscuit tins often are repurposed to do (you see the specialization that keeps the name "biscuit" attached to them).
So, yeah, I think the difference in emphasis is there, but term "biscuit tin" also ends up suggesting something a bit more specific than a biscuit "container" or "box".