Thank you for your help and enlightenment, everyone. ;) Some final questions, though:

Is it possible (or easy enough) to add just some tweaks or pre-included software to a certain distribution? Or start from a certain distribution and add or remove the default software to suit my needs? I realize this may be possible using Gentoo or some of the more modular distributions you've mentioned, but is it possible to do a personal version of Linux Mint, with the programs I know I'll need?

And when it is said that a certain distribution is built off another what does that mean exactly? Linux Mint is built off Ubuntu, which is itself built off Debian, what does that mean in terms of things they have in common?


Cheers

Yes, you can install almost all software on all distributions. And there are tools out there to create your personal respin, like remastersys.

That does mean that the developers use a different distro as their base. That is easier than building the whole distro from scratch. For example, Mint is Ubuntu with some packages recompiled, some extra packages and with a different default package-set. But you can install Ubuntu's packages in Mint. The same is true for the Debian editions of Mint.
But because Ubuntu nowadays is not so close anymore to Debian you shouldn't install Ubuntu's packages in Debian and vice-versa.
In general that commons are the package management system and some of the administrative tools.

It mostly means that they share a set of core tools and the same package manager. Building a customized version of a given distro might be harder or easier depending on the distro itself. Some of them might provide docs and tools on how to do that (Gentoo has catalyst, for example). There's no generic response to that question.

It means that instead of making their distro from scratch, they took the existing base distro and modified it.