There are a lot of variables making up a sound. The guitar, amps, speakers, and any effects pedals, all colour the sound in some way. In a guitar, the pickups will make the biggest difference, but not as great as changing an amp (or channel), or throwing most effects pedals in the mix. Changing speakers might be on a par more-or-less with changing pickups.

As well as the different types of pickups, the main things that make similarly laid out pickups (i.e. two humbuckers) sound different are magnet type, wire gauge, and number of times the windings are wound. Generally the more windings the higher the total output voltage (louder signal) with a reduction in mids.

But anyway, hearing subtle nuances between how different guitars sound is a bit like taste. When you first drink wine you might be like, "ew gross, that's pretty horrible," and they all taste very much alike. Then it's "oh, this one's okay," or "that's actually a nice one". Eventually you're like "ah, what a wonderful medium-bodied garnet, with whispers of lavender, tulips and cacti!"