Within a given model line (say we are talking about the Seymour Duncan JB bridge humbucker), the only difference is supposed to be that the trembucker is ever so slightly wider on account of the pole pieces being ever so slightly farther apart. I say supposed to be as I am curious myself if there is a measurable difference in tone, given that you would have to either use slightly fewer turns to achieve the same DCR/output, or you would use the same number of turns and have a slightly higher output and slightly more rolled off high-end. I think any difference we're talking about here would be in the +/- 5% range, but that is on my list of things to look into once I have a pickup measurement rig working. Other manufacturers may refer to this as "F-spacing" (that is how DiMarzio calls it), and others don't offer this option at all.
So why was the trembucker created at all, and why doesn't anyone talk about playing trembuckers? Classically Fender bridges had/have a wider string spacing than Gibson bridges, approximately 2.07" (53mm) vs. 1.93" (49mm). If you put a standard-spaced humbucker in the bridge position of a Fender-spaced bridge guitar, you will see that the highest and lowest strings (especially) will not be centered on the poles of the pickup on the 1st and 6th strings, slightly decreasing output. The trembucker is designed to have pickup poles that fit (for the bridge position) directly under these slightly wider-spaced strings. Note that this is only relevant to bridge pickups, as though the neck strings on these Fender-spaced guitars would also be slightly wider, the strings would have started to converge a bit more and it is generally thought to be less of an issue.
If you don't know what string spacing is or how to measure it, click HERE to check out a quick article on it.