What are Stands?

I've seen many definitions so far, embodiments of one's willpower, of one's soul, and the basic definition of one's... "ability." It states in JoJo's that they're specifically embodiments of one's willpower.

But what does that make of stands that have no specific user like Survivor and Notorious B.I.G.? To clarify, both of those have users, but they don't follow their will, B.I.G. just tracks movement and absorbs, Survivor just infects people with rage.

Or ones that can switch users like Superfly and Cheap Trick, the latter of which has a mind of it's own. There's so many more, so what really are stands, if those aren't just exceptions? And does the embodied willpower really mean if stands like Cheap Trick have such murderous intent to their user?

My main question is, how does willpower from yourself become a stand? But I'm not asking about arrows and the virus from the meteor. I know that personalities define it. But does that come from one's soul?

And does that make stands come from one's soul if the energy of the stand coming out can have so much of an effect on people? Since damaging a stand causes the user to be damaged, that's direct life-linking between the two. But what does it mean for independent stands?