Just as sort of a caveat about this idea of "training" (because I think it plays a big role, to some extent).
There are basic principles to sound production which people whom are being trained by
good teachers, in any genre of vocal music, will learn. All singers will learn how to support their sound with their body and breath, and this will consequently bring about a "certain" sound and characteristic to their vocal production -- that wouldn't necessarily be there if they didn't have training.
The funny thing about that is that the kind of breath and bodily support a person
learns to give to their singing is something that has actually already, at one time, just come more naturally for all of us.
I have been in several weeks worth of a vocal classes (incognito at first

) where the target student was not the Opera singer. People from all walks of life were in this class and they were each encouraged as individuals. However, the focus of the class was on sound production, though a number of people brought their own "popular" music to sing. There were several things we did in there to tap into our "natural" sound, but everytime somebody did that, though there was still an individuality to it, there were also basic, shared qualities between individuals, about the sound itself -- whether they were man or woman and no matter what the intention (as long as it was "true").
Two of the most naturally "well produced" sounds we each have made in our lives is crying and laughing when we are a baby. We are built to make these sounds and these sounds reflect a true intention (which is part of the deal). If you have a room full of 20 babies crying or laughing, believe me, they will all sound the same unless one of them is your's (the reason you would care about the differences) and you know,
specifically, what you are listening for.
Unfortunately, after being a baby we undergo years of "conditioning" as we grow up, affecting us psychologically and in turn, physically. We forget how to carry ourselves, we forget how to talk, we forget a lot of things. I think sound production "training" is more or less a mere reminder of stuff we already know/knew at one time (but that can be very tricky).
The point is, though, that the more natural/trained (ironic) a voice, the more similar will be its characteristics with other voices. The biggest show of nuance and "differences" will be the particular repertoire and how this highlights the strong points of an individual's particular voice (and strong/weak points will vary with each individual and "voice type" -- voice type basically being a categorization of what an individual's strong points and weak points are).