I've written code (professionally and as a hobby) for the kernels of the various flavors (including Windows and Mac) and they all do exactly the same thing: allow me, as a developer, to not have to write my own operating system.
Personally I regularly use OpenBSD, Slackware, Debian, and have a slew of VM's that have the various Linux versions, though my personal favorite is TurboLinux. And as you've noted, a lot of the various distro's are actually based off of one another; that Wiki link actually has a pretty good "family tree".
Answering your questions directly:
- What distinguishes the different Linux Flavors?
There's a few things, but typically the "biggest" differences are the kernel version used, the package manager used (if any), and the system configuration (like if it uses SELinux by default, or uses the /proc/ file system, etc.).
You also can't necessarily just take a program built in one Linux and run it on another; that is, you can't necessarily take a program built on Ubuntu and expect it to run on Zorin. Though that's something for the developer of the program to consider and not really you as the user.
- What distinguishes the different distributions that are based on a common flavor?
As you've noted, typically just the GUI and programs that are installed by default; but as with most distro's, you can usually download a 'minimal' subset, which is just the kernel and base set of packages the OS needs.
Side note though, after systemd came about, there have been forks of Debian that are systemd free, so that's a difference, but only something you're concerned with if you're actually concerned about that.
It's up to the distribution distributor as to what they'll put in it, so it could be almost anything that differentiates it, but in my experience (at least over the last 20 years), the biggest differences are usually just the default desktop environment and default system setup.
- Is there a difference between, say Xubuntu and Lubuntu, beyond choice of desktop environment and associated packages?
Specifically between Xubuntu and Lubuntu, not really, see point 2 above.
- If I install the Ubuntu minimal image and then install a desktop environment of my choice (or multiple), e.g. aptitude install lubuntu-desktop, what is the different between that and installing Lubuntu? If I install the Cinnamon desktop, then other than the list if pre-selected packages, how does that differ from installing Linux Mint?
You've nailed exactly what each "distro" is; just a pretty package on top of what you can do your self.
The difference in this case really boils down to "branding". If you do a uname -a it would probably say "Ubuntu linux86_....." versus "Lubuntu...." .. that and the source to which you download your packages from (e.g. Ubuntu based distro's would use the Ubunto repo, RedHat based distros can use RedHat repo's, etc.). Anecdotally, according to the wiki (and personal experience), before it was a full distribution, Lubuntu had to be installed as a separate package on top of Ubuntu!
As a cross-platform developer, I also regularly use Windows and macOS.
The absolute biggest difference between every single OS: the programs you can use; some work on Windows, some on Mac's, others on Linux, and some need an embedded OS. There might be a ton of Linux's (Linii??), but in the end, it comes down to if the program you want to use actually works on the OS you have.
Hope that can help add a little clarity.
A distribution can use any criterion it chooses to differentiate it from any other distro. The desktop environment is a common differentiator, but there are an infinite number. An then there's the one-off custom builds. – sawdust – 2017-07-04T02:51:37.113