Well, almost. When you pick up a linux distro you expect the linux distro to be using the kernel, or some variation of it, that is maintained by Linus Torvalds (or whoever is maintaining an older kernel). With UNIX, they may all have different kernels. They probably all started in the same place but branched from eachother and have different code bases now.
I think you would benefit from reading this
. It is the story of UNIX from Bell Labs. I enjoyed it when I first read it. You might want to read about the creation of Linux too. You can google for that I'm sure.