I typically search the package name + fedora, it will probably tell me the alternative package that is in fedora.

Nowadays, I have moved to an atomic fedora distro, so I would severely limit the amount of package I install on my system for stability and security.

I think I only have two packages installed on my machine: fish, because it is the only popular shell that follows xdg dir; and a latex-like input method to use in slack.

Try paveaucontrol, it has an option to lock settings plus it's a neat app to call when you need to customise settings. You could also add user to the group that has access to mic.

No never! Do not use Kali as main OS choose Debian, Fedora, RHEL (not designed for this use case) or Arch system

The practical difference is the package manager; Debian-based systems use dpkg/APT with the .deb package format, Arch uses Pacman with .pkg packages.

Debian-based distros use a stable release cycle, so there are version numbers. The ecosystem is maintained for each version for an extended period of time, so if you have a workflow that requires a specific era of software, you can stick with an older version of the OS to maintain compatibility. This does not necessarily mean the software remains unpatched; security or stability patches are applied, this tends to mean the system is stable. Arch-based distros use a rolling release, basically what they said they were going to do with Windows 10 being the "last" version of Windows and they'd just keep updating it. Upside: Newest versions of packages all the time. Downside: Newest versions of packages all the time. You get the latest features, and the latest bugs.

Debian-based distros don't have a unified method of distributing software beyond the standard repositories. Ubuntu tried with PPAs, which kind of sucked. Arch has the Arch User Repository, or AUR.

Arch itself is designed to be an a la carte operating system. It starts out as a fairly minimal environment and the user will install the components they want and only the components they want, though many Arch-based distros like Manjaro and EndeavorOS offer pre-configured images. Debian was one of the earliest distros shipped ready to go as a complete OS; I know of no system that offers the "here's a shell and a package manager, install it yourself" experience on the Debian family tree.

But given an installed and configured Debian and Arch machine, what can one do that the other can't? As in, can it run [application]? Very little.

You can “do” the same thing in Debian as you can arch, the main difference is packaging philosophy, Debian packages are older and more stable, while in Arch world you typically have the newest version of software packages as late as a few weeks from their release (the caveat being breakage is a bit more likely), Arch also has user repositories where the community can contribute unofficial packages