On this thread I give some background on how pickups work. There are a lot of factors that determine what a pickup sound like - type of magnet material; size, orientation, and number of magnets; number and orientation of coils; size of wire in the coils; the spacing between the parts; the loading impedance presented by the controls (just to name a few).

Then you have to consider the guitar. In terms of vibration, it's a very complex system, with contributions from the materials used, and how they are put together (I really simplified that part!).

To (try to) answer your second question: maybe.

Some pickups, like EMG 81/85s, tend to 'swamp out' the tone contributed by the guitar, so they sound pretty much the same in any axe.

Ohters, like DiMarzio PAF Pro or Tone Zone, derive a lot of their sound from the guitar, so any differences are going to show up in the sound.

The biggest factor is the [u]player[/u]. Get six people to play the same piece of music with the same guitar and amp and you'll get... six different sounds!