Pickups are basically a device that has been produced through mechanical processes. Some variables such as number of windings around the magnets give different models different characteristics.
Personally, I find that only the weirdest and most unique pickups from specific brands are identifiable through a double blind test... Anything that wanted to emulate some vintage pup with a "sparkle" sounds similar regardless of brand... All the descriptions of the pups you read online on the pup manufacturer's sites are nearly total bull. The brand/model of pups lives on mojo that's where all the long story and history comes in on the site's description.
Basically there're a few groups of pickups with similar characteristics:
single-coil size:
vintage with extra trebles, vintage, modern with much less trebles, and respective humbucking silent variations. some are even humbuckers in single coil sized pups etc.
humbucker size:
vintage humbucker types, modern humbucker with extra high outputs, humbucker that emulates single coil trebles with low outputs, modern humbuckers with boosted mids etc.
There're certain unique models that fall into one of these categories and have unique tone but its hard to explain what one hears unless you try them out! mmm pups are where all the mojo are! haha =)