Different person, but I’ll try to explain some of what I know.
Traditional Linux:
read/write root and usr
only one version of a program can exist*
packages are available immediately after install
packages are imperative (you tell it what to do, it does that)
files swapped in place (can lead to issues like kernel modules missing or Firefox not opening new tabs until restart)
*you might have python3.8 and python3.9, but those must be created as different packages using different paths in /usr
NixOS, Guix:
declarative package management (basically config file and exactly these packages are installed)
usr and parts of root read-only (afaik)
packages symlinked to usr
multiple versions of packages kept locally (though not all active necessarily)
will keep using old package until restart/reboot, therefore not breaking on updates. New instances of a program can use the new package
easy to roll back due to multiple versions kept
Immutable OS (haven’t seen one mentioned by OP, but it’s a category):
often imperative package management
using snapshots or multiple root partitions for easy rollbacks
read-only root and usr
packages might only be available after a reboot (depends on implementation and if system packages or something else like Flatpak, which doesn’t need a reboot, are used)
SerpentOS:
experimental distro (ie stuff might change)
imperative package manager
packages installed to separate tree, but swapped live. Basically A/B root of an Immutable system that doesn’t require a reboot (according to the explaination in the latest blog post)
Not sure why ClearLinux is on that list of special distros and I don’t know half of the rest so yeah. Hope this explains some of it?