There is no "Win_L" or "Win_R" in /usr/include/X11/
keysymdef.h. (this is a file that has all possible names for keys on the keyboard). Thus it is impossible to execute the
xmodmap commands shown above. Some symbol from keysymdef.h had to be chosen.
For most of Linux history these keys were given the names Meta_L and Meta_R. But it appears Emacs messed this up, the appearance of these symbols in the keymap would cause it to stop obeying Alt as the "meta" key (this would happen even if you had an old keyboard that lacked the Windows keys, making Emacs useless!). So at some point around 1998 it seems the default was changed to be Super_L and Super_R, which avoids this problem, but it broke programs that assumed these were Meta. Sometimes the right-hand key is MultiKey just to make things worse.
The other "Windows" key with the menu on it seems to be assigned the Menu keysym on all Linux systems I have seen.
Though I greately preferred the name "meta" it looks like it is best if you program these two keys to be Super_L and Super_R.
Almost all X servers seem to agree that these turn on the shift flag 0x40, so if you just want to see if the key is held down you can look at that.