It seems to me that "mutig" and "tapfer" are virtually perfect synonyms.
The course test on both with the identical question:
"Er ist ____ wie eine Löwe." (He is brave like a lion.)
The answer desired is either Tapfer or Mutig.
They are not accepted as synonyms. In each case only one or the other answer is accepted. Both answers fit more or less equally well in the answer block. So far as I can see, there is no way to tell which answer will be accepted any given time this question comes up.