Red shoes by the drugstore

Something puzzling—here we see "Der Lindenbaum", elsewhere titled "Am Brunnen vor dem Tore", after its first line, attributed to Wilhelm Müller.  But we also see two different, though more or less equivalent, Latin versions (I prefer the one on the right).  What's the relation?  Did Müller write it, only to see it translated into Latin?  Did he translate it out of Latin?  Are they all folk songs originally, and Müller collected the German one?

That very site provided the text when I wrote about the song for a class on The Magic Mountain lo these many years ago.