Android is Linux, even if it doesn't follow the philosophy of your favourite Linux distributions. Maybe RMS had a point when suggesting people call it GNU/Linux. Maybe Android/Linux?
Yep: GNU/Linux is very different from busybox/Linux is still different from Android/Linux, because the userland is (often) more important than the kernel; a user of Debian GNU/Linux has more in common with GNU/kFreeBSD than Android/Linux.
Yes, it's a very different experience running Android with Amazon's setup on a Fire Device than on with Google Play Services, even if it's binary compatible.