I wrote "He is better than I" and it was marked wrong; correct being, per Duo, "He is better than me", which is absolutely grammatically incorrect....
Is there a difference between 'He is superior to me' and 'He is my superior'? I would have thought that they meant the same thing, but the latter was deemed wrong.
"he is superior to me" means that he is better than me (in whatever matter)
"he is my superior" means that he is my boss
Yes indeed and of course the boss is very often inferior to the workers in ability.
Making him an inferior superior.
"Superior to me" does not ONLY mean "better". It can also mean having a higher rank, particularly in the military.
Then how do you translate "he is my superior" (I wrote it as the translation for the French sentence which was wrong, of course)
Simply because if you back translate it, the sentence has to change: he is my superior = c'est mon supérieur.
"he is better than me" accepted BUT grammatically this is incorrect and should be "he is better than I" (am). this has already been pointed out below.
I believe you can also use the indirect object pronoun, me.
Il m'est supérieur.
I would never say, "He is better than me." Totally incorrect English grammar. "He is better than I" is correct because you would say, "He is better than I am." Not "me am." Grrr!