GNU was an OS project choosing to emulate Unix, without a specific hardware goal.
Linux was an OS project focused on running itself on the Intel 80386 processor.

GNU started in 1983, and Linux started in 1991,

Idea 2: Linux based GNU systems

GNU is a Unix inspired free OS that is almost completely distributed with the Linux kernel.
While the GNU project chose to

Idea 3:

Blacklight OS is a free POSIX-compliant OS distribution running atop Linux.
The first such POSIX-compliant OS was GNU, and Blacklight OS is proudly following in its footsteps.

Blacklight OS is a distribution containing the following parts:

Ice Cream Theory C Library
Toybox System Utilities

Blacklight OS depends on the following free software:

FreeBSD Operating System (For its C Library)
Toybox (For its System Utilities)

Idea 4: Like Windows

Early versions of Windows shipped the POSIX subsystem, which was alongside the Win32 subsystem, the OS/2 subsystem and the security subsystem (Access Control).

So, NT could implement both the POSIX OS and the Win32 OS. But it has removed the POSIX subsystem since Windows XP.

So, Win32/NT, POSIX/NT, GNU/Linux.
GNU/Linux would simply be POSIX/Linux.

POSIX/Linux could be called chuckles Lunix.
Ubuntu would be a Lunix distribution.

Distribution / Product	OS
Microsoft Windows	Win32/NT
Apple macOS	Darwin UNIX/XNU
Debian GNU/Linux	GNU POSIX/Linux
Canonical Ubuntu	GNU POSIX/Linux
Fedora Linux	GNU POSIX/Linux
Red Hat Enterprise Linux	GNU POSIX/Linux
Alpine Linux	GNU POSIX/Linux
Arch Linux	GNU POSIX/Linux
Void Linux	GNU POSIX/Linux
SUSE Linux Enterprise Server	GNU POSIX/Linux
Gentoo Linux	GNU POSIX/Linux
Slackware	GNU POSIX/Linux
Google Android	Android/Linux
Google ChromeOS	Chrome/Linux
FreeBSD	FreeBSD POSIX
OpenBSD	OpenBSD POSIX
NetBSD	NetBSD POSIX

Left-click: follow link, Right-click: select node, Scroll: zoom