The meaning of the word "inappropriate" somewhat changes depending on context.
In the sentence
In an email reply to my professor, I misunderstood what he told me and
wrote something inappropriate.
the word means something that is at least a little insulting, hurting or irritating in a negative sense.
When I say the use of "inappropriate" in the text is inappropriate, that does just mean the word is not used in the right manner, with no further implications.
The correct meaning (assuming no rudeness, insult etc) with only one word changed would be
In an email reply to my professor, I misunderstood what he told me and
wrote something wrong.
It can be written in nicer forms, but this is a modified example from a real question text.
I think the best example of this effect, is the word, "fuck".
It can even have context dependence on the voice modulation!
I am sure there are many examples - write as comments if you like!
So, are my assumptions right?
Does this context dependent meaning change have a name?
Is there some more formal description of it?