What are all these other types of Linux commands? I only know Debian those seem like something else.
If you only care about using Linux Mint or something else based on Debian or Ubuntu, you do not have to know anything else outside the distro you are using. It's because it could become the source of confusion.
Do you want the bleeding edge in software? Do you buy a new computer every year? Are you willing to make adjustments to your system so it's "just right"?
If you have answered "no" to all three questions,
you do not have to care about what another distro has which is not fully compatible with Debian or Ubuntu.
Let me tell you a few things. This "yay" was invented because apparently "pacman" wasn't good enough. People become interested in Arch Linux to install stuff found in the AUR, they keep being told it's at their own risk, then when the system breaks they want to blame the operating system. This "yay" apparently wasn't enough so like three, four or more other "AUR helpers" were invented, and it must have been for a reality show about coding in Python.
If you are going to try a different distro, you have to be careful with any of them that use RPM package format: Red Hat Enterprise Linux, Fedora, Mageia, OpenSUSE, PCLinuxOS, ROSA etc. I don't want to go into any detail, but it's easy to become frustrated with RHEL and direct descendants taking years to change stuff (eg. GNOME behind in version), and a rolling release otherwise out of this group.
(EDIT: I read somewhere that "yum" was obsoleted, at least on Fedora, and it remaps to "dnf". OpenSUSE has "zypper" which is a little bit better. However all of those could be slow unless the user has a fast Internet connection.)
Then there are others like Gentoo and Slackware which aren't for people who quit easily. Slackware does have GSlapt GUI combined with "slapt-get" command-line utility for handling program installation, upgrade and removal a lot like Synaptics on Debian, but it's not "official", and it's not known if Mr. Volkerding would give the go-ahead to make it part of Slackware for v16. Without GSlapt, "you're on your own" installing and removing stuff! In Gentoo, software is usually compiled from source which could take a long time. Somebody who's a programmer doesn't set up stuff right could cause a compilation failure, and therefore inability to install a program. Also this "USE" flags that have to be adjusted according to the capabilities of your system. I don't dare say anything else... this paragraph should have been shorter.
I'm not writing this to discourage you from learning or from using Linux. If you plan to stay with Linux Mint or other Debian- or Ubuntu-derrivative, you could find out stuff that apply to different OS's, but then store it in the library.
One more thing. Do not apply any terminal command line, and do not install any program, suggested on sites like "keep pouring the syrup, too much so I drown" (sorry must write it like this) unless you're absolutely sure you want to do that, and more importantly, you know what you're doing on your system. There is a topic in another site about doing kewl things with "bash" scripts and that sort of thing. Do not go there unless it's what you want to do and you assume full responsibility for system misbehavior afterward.
