Linux

This is a great question!

It's hard to really wrap your head around it without doing a ton of low-level taking things apart and putting them together differently.

But to answer, it's pretty impressive the extent to which a full Linux install of any distro tends to just be like a bunch of legos put together in one particular way.

Theoretically, there's no reason why you couldn't ship-of-Thesius one distro into another. You'd have to have a good idea of what the differences between the two are, but it can certainly be done.

There's a thing called a "chroot." It's basically a whole OS installed in a subdirectory on another whole OS. And there's a command (also called "chroot") that can be used to tell the parent OS to "give me a shell in the chroot OS -- as in run the /path/to/chroot/bin/bash (or whatever) executable in 'The Matrix' such that that process thinks that the chroot is the root OS.") That lets you do some pretty cool stuff like building an OS to be installed on another box. But when you run in the chroot, it doesn't load the guest OS's kernel or (typically) init system or anything. The processes run on the host system's kernel.

And it's entirely possible to have the guest chroot system be a whole different distro than the host. (Though some distros will have tools that make it easier to chroot into a guest chroot of the same distro.) Which implies that you can just kindof substitute one distro's kernel for another distro's, right?

Turns out the answer to that question is "at least mostly yes." Quick funny personal story. I started working somewhere recently where they allowed new hires a choice between Windows, Mac, or Linux on their work laptop. I chose Linux, but didn't like the distro they pre-installed on it. (KDE Neon. I preferred Arch. Insert hate here.) But the laptop had secure boot enabled and the PC support department wasn't willing to let me disable that. The laptop would only allow certain kernels to boot. Windows and some kernels from some unknown set of Linux distros.

Just as a quick aside, the way it knew how to deny a specific kernel from running or allow another to run was with signatures. Canonical which makes Ubuntu includes cryptographic signatures in the kernel file identifying that kernel image as made and certified by Canonical. (Microsoft does roughly the same thing for Windows kernels.) The secure boot system on the laptop has a list of trusted certificates. If the kernel that the bootloader (which is also signed, by the way) asks the secure boot system to boot is signed by one of those certificates, it boots. If not, secure boot denies the request. Theoretically more certificates can probably be configured/trusted, but that wasn't an option in my case.

But I still wanted to run Arch! Now, KDE Neon uses the Ubuntu kernel, so I knew that was one I could boot without access to the secure boot config. So I grabbed the .deb for the Ubuntu kernel, wrote a script to convert the .deb for the Ubuntu kernel into an Arch package. (Arch doesn't use .debs or .rpms. It uses "pacman packages".) I installed that arch package, configured the bootloader to point to the arch install including that Ubuntu kernel, and booted it. Viola! Arch (mostly) without secure boot access!

What I was running was really kindof 95% Arch and 5% Ubuntu kernel. Kindof a Frankenstein's monster of OS's. But it worked perfectly.

And theoretically, just about any part of a distro can be replaced with the equivalent from another distro. (Or from the upstream/source version.) You could technically take a Fedora system and replace the package manager with apt (I'm guessing there isn't an rpm package that would install apt on your Fedora, so you might have to make it yourself or just build it from source and install it manually) pointed at Ubuntu repositories and transform Fedora piece-by-piece into Ubuntu. It'd be a pretty wild and messy process. And it would probably be easier to just reformat and install Ubuntu. But it could be done.

Similarly, you could replace the init system. Artix is a fork of Arch that gives a choice of init systems whereas Arch only supports Systemd. And it's kindof another Frankenstein's monster of an OS because it still relies heavily on the Arch repos. But it works.