Linux Mint would be an OS built on the Linux Kernel.

Some people have a hang-up on calling any Linux kernel based OS “Linux”, because unlike its competitor, there is a lot of OS flavors.

You have “main” OSes (Debian, Fedora, etc.) and derivative OSes based on these “main” OSes.

Linux Mint for example, is based on Ubuntu, which is based on Debian.

At this point, it is semantics.