Most communities that I see have very straightforward names like 'asklemmy'. I have also seen '/c/showethoughts'. What does the '/c/' mean here?
Okay, but then I still don't get why the '/c/' part is only showing for /c/showerthoughts (see screenshot).
I'm guessing the user who created "/c/showerthoughts" named it "/c/showerthoughts". You're seeing the community names, and that one is named the same as the URL.
Unnecessary, yes. In error, maybe or maybe not. Some people just may not want to come up with a name apart from the URL and decide to use the URL fragment as the name.