Android is based heavily on the Linux Kernel and has used many of the linux command line tools. If rooted you can even run busybox on it, in conjunction with a terminal app, to get a full linux command line experience out of it.
iOS is based on a highly modified Darwin (the underlying OS which OS X essentially runs as a GUI on top of), Darwin essentially stole a combination of FreeBSD and BSD-Lite which. BSD is one of the original Unix systems.
Since Linux is a Unix-like operating system, you could argue that both Android and iOS are mobile *nix implementations, yes.
Apple pulled a fast one with OS X when it first came out. The BSD license says essentially that you can use all of its code, as long as you publish your work for free. Apple was devious, so they stole essentially the entire underlying BSD OS and - with some minor modifications - called it Darwin, and then wrote the GUI as a closed source proprietary program that runs on top of Darwin. In keeping with the BSD license, anyone can download the Darwin source code without the OS X GUI for free (but no one really wants to, because without the GUI, and without the FreeBSD GUI, it is kind of useless. The GUI is closed source and not shared under the BSD license.
So Apple essentially used a lawyerly loop hole in the BSD license to steal the entire underlying BSD code and build a proprietary OS on top of it, which IMHO, really isn't cool.
Interesting bit of history...hadn't heard that before, although I know Apple has a long history of borrowing good ideas.