What are some Linux distros built for specific jobs?

For repair and recovery, take a look at Trinity Rescue Kit. It's intended for tasks like repairing Windows systems and recovering data. Clonezilla also has a bootable Linux environment focused on cloning drives.

Those are handy examples of distros you might boot for one job rather than use as an everyday desktop. Check carefully which drive is the source and which is the destination before cloning.

IPFire is a neat one if you're interested in networking. It's designed to turn a computer into a configurable network firewall, rather than serving as a general desktop OS.

NixOS is interesting for reproducible setups. You describe much of the system in configuration files, including packages and services, rather than treating every change as a one-off command. That makes the configuration useful when rebuilding a machine or setting up another one.

GNU Guix is another declarative option worth exploring. Both have a learning curve, especially if you're new to Linux and also learning their configuration languages at the same time.

Gentoo is a good pick if the goal is to customize the system deeply and learn how its pieces fit together. Its traditional approach involves compiling packages from source, which gives you choices but can take a lot of time. There are also precompiled packages available, so compiling everything isn't the only option.

MiniOS is worth a look alongside Puppy. It's aimed at running from USB, with persistence and system modules loaded into RAM. It also has tools for making modules and customizing an ISO, plus support for separate sessions with different configurations.