Force quitting apps vs gracefully quitting apps on Mac

What differences are there in the processes that occur when either CMD-Q'ing an app vs force quitting it?

Essentially those you described: give the app a chance to "save" its work and temporary files so that it can launch quickly the next time. Also, the app should release system resources upon quit to be made available to other processes that need them. However, since lazily written apps are the norm rather than the exception, macOS versions going all the way back to Snow Leopard already has the ability to kill idle processes (within limits), releasing system resources such as memory, file allocations and CPU time, meaning there's effectively no difference between quit and force-quit in many cases.

Besides, the concept of explicitly having to "save" your work is gone in all Apple apps and most of the better written ones. In fact "autosave" is part of that automatic termination process. Taken to its logical conclusion the fact a Dock icon might have a dot under an app indicating it's "running" means very little. An open, apparently "running" app may already have had the processes associated with it killed by macOS, only to load them again should it become active. You literally cannot tell the difference.

Have you ever asked yourself how to "quit" an iOS app? Has an iPhone ever lost your saved work? Didn't think so.

Likewise, what damage would be done to an app if it was force quitted, if any?

To the app? None. You might lose "unsaved" work, and to cite a trivial example consider virtualization software. If you force a VM to quit it's gone, whereas quitting the virtualization software nicely gives it a chance to save the VM first so that it can be reloaded when you restart it.

Is it possible that the finder could become corrupt by force quitting it many times, requiring a complete reinstall of macOS to fix it?

No chance whatsoever.

So go ahead and force quit if you like.