Specifically, I'm looking for the term for when a person uses a word correctly, but intends a different meaning.
I empathize with you.
When the person really means:
I sympathize with you.
Both sentences are grammatically correct. They both have meaning, and as sentences they are both "correct"...they're just incorrect in this case.
This isn't a case of a malapropism where a similar sounding word is inserted with ludicrous results, nor is it a parapraxis, eggcorn, or mondegreen (as I understand them). It's simply a case where a person either misunderstood the difference between the two and thus chose the wrong word or the person did understand but believed (in this case) they empathized when in fact they only sympathized.
I'd like to say something like "You made a grammatical mistake/error" - except in this case it isn't grammar...