What software do all linux distributions have in common?

A little context: I recently installed Arch Linux on a chromebook through a bizarre hack in which I used an install script to install Ubuntu and then overwrote the Ubuntu rootfs with an Arch rootfs. I'm not sure what the mechanics are behind this (like this: https://wiki.archlinux.org/index.php/Acer_C7_Chromebook) . Is the part of Linux that runs before chrooting into rootfs common to all Linux distros (and that's why the initial boot worked for both Arch and Ubuntu)? Or, to be more general, what pieces of software are common amongst all Linux distributions, i.e. define a Linux distribution?