What it comes down to I think is playing music is just another form of self expression. You can recognize somebody's writing by their penmanship or their sentence structure and word choice. You may recognize them by their speaking voice or their phrasing. Music is the same.

What's unique and amazing to me regarding technique and style with the guitar is that you can recognize a player just from a single note. Everything that has been mentioned in this thread (physical feel, equipment, personality, etc.) can come together in one single note (OK, maybe 2 technically if it incorporates a bend or crazy vibrato). Players like SRV, David Gilmour, BB King come to mind.