My kernel version is ‘6.8.0-87-generic’ and hers is ‘6.14.00-33-generic’. My brother, who uses CachyOS, has kernel version ‘6.17.1-2-cachyos’. So it makes a little sense that the kernel is different. Even though I always thought that there was just one kernel that all Linux versions use.
But why is there a different kernel for the same distro?
Mint has two kernels: a “stable” one and a “hardware enhanced” one (HWE). The HWE kernel is newer to improve support for newer hardware.
Many distros allow you to pick from multiple kernels.
Yes, all Linux kernels come from kernel.org
That said, kernel.org maintains not only a latest but also multiple “stable” kernels that maintained versions of previous kernels. There are usually about a half-dozen kernel versions to choose from.
One you have code from kernel.org, you can change the configuration to get kernels with slightly different capabilities and strengths.
Finally, you can patch the code you get from kernel.org to add or remove whatever you want. For example, you may add in filesystem support or drivers missing in the mainline kernel.
So, in the end, any given Linux distro may have a Linux kernel slightly different from what other distros use. You can probably run any Linux distro on the kernel from any other Linux distro though. In fact, this is what you are doing when you run something like Docker or Kubernetes.