So, I downloaded an older version of tb and stuff just to have it..
But it replaced my Steam version from my desktop and I don't know which
one to get back on my desktop as there are two Toribash applications in the
Toribash Steam folder that both open Toribash to the current version.
One is called toribash.exe and the other is toribashSP.exe

So, question is: Which one do I create a desktop shortcut of and what's the
difference?

ToribashSP is used to open replays (so that you didn't have to close the game if you are playing), you need a shortcut of toribash.exe

Ok, I created a shortcut of it, but now toribash.exe is not working....
toribashSP.exe can still be opened, but not the other..

Wait, so did you replace the toribash.exe from the Steam version with the old one?
If you did then it wouldn't work, you need to check the cache integrity to fix it.

No, I merely downloaded and installed the older version. I didn't touch any files.

You can close this.. I just re-installed it and changed the shortcut's name to "Toribash Steam"
in case of future mishaps.