I can definitely confirm that not everyone knows what they're meant to be or why you might want one over the other. 🙂
What I'd suggest is what I'd always suggest when someone is looking into buying something, which is to find reviews of the thing you're thinking of buying. For plugins which emulate famous pieces of gear, reviews will normally tell you which one they're emulating, and will often talk about what's special about the hardware in question and whether or not the plugin gets that right.
I don't know of any resource which tracks which emulations are which, but the clues are often there. To use Waves compressors as an example:
The PuigChild 670 is a Fairchild 670 emulation
The CLA-76 is an 1176 emulation
The CLA-2A is an LA-2A emulation
The V-Comp is a Neve 2254 emulation
The dbx 160 is a dbx 160 emulation 🙂
Sometimes you have to dig into the descriptions on the site to find the clues (as in the case of the V-Comp).
As for what you'd best use them for, I'm nowhere near an expert on that, but that's one of the reasons why the academy and the courses we get here are great; you can see e.g. Bob Horn using an 1176 emulator on a pop vocal and now you know one thing that an 1176 is good for, which will be good for any 1176 emulation no matter who makes it.
Plus messing around with stuff is good. Put one option on a track, and if you don't like the sound, try a different one.
I hope this sheds a tiny bit of light. 🙂