Richard Stallman intended GNU to be a full-fledged operating system, but without a kernel, he couldn't do it. At least until he discovered Linus Torvalds' Linux kernel, thus the GNU/Linux (or GNU+Linux) operating system was born.
As far as open-source projects are involved, both are open-source projects. And you don't have to only use the Linux kernel with GNU, as there's the GNU/Hurd project, and then the ever-popular Android (runs on a modified Linux kernel, the remaining are developed by Google)
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