All Linux system are essentially same: they all uses Linux-kernel. The differences are the ways in which kernel is compiled and OS communicate with it. One can install any of them and do whatever one can do on some other Linux system. Ubuntu is perhaps the easiest to use, and
Gentoo is perhaps the hardest one. Between them there are dozens others one can pick.
On lab machines, one encounters fedora, centos, suse (and other related OS/Distros/Whatever); they are popular for servers machines. Some of these distributions runs extensive test before a package is pushed to their stable repositories. It reduces the risks of "breaking the system" on system update. Many CAD vendors supports only Fedora based machines.
Puppy linux (and Damn Small Linux) are cute little creatures. Puppy is around 125MB and DSL is about 50MB is size, yet they are fully fledged OS. DSL is ideal to keep on SD cards and other tiny devices while Puppy is ideal for usb-sticks and external hard-disks. One keeps his OS and data in his pocket. If a system BIOS is not protected, then one can simply boot the machine from usb stick. It is ideal for recovering a broken machine, but much more can be done with it. Slacko Puppy is great and quite stable. I dont have good experience with Precice Puppy (it allows installing Ubuntu packages). Puppy can create its own file-system on external disk (called sfs), one can copy this sfs to any other puppy and woila, the data and installed packages are back. Much like virtualbox files.
Gentoo is a different kind of beast (perhaps Arch-linux is somewhat
similar to it). The major difference between Gentoo and others is that
one does not install pre-compiled "packages" on Gentoo, source code gets
downloaded and one builds the binaries on one's system. This usually
makes machine faster (like 5-10%, big deal) but on servers it can make a
huge difference especially when you have the freedom to tweak and
compile the kernel. Gentoo is also good for pedagogy. One can play with
it in Virtual-box to know the gory details involved in making a OS boot
and work.
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Dilawar