The literal meaning of a word is its denotation; the broader associations we have with a word are its connotations. People who depend on a thesaurus or a computer translation engine to find synonyms often choose a word with the right denotation but the wrong connotations.
“Determined” and “pig-headed” both denote stubbornness, but the first connotes a wise adherence to purpose and the second connotes foolish rigidity.
“Boss” and “Chief Executive Officer” (CEO) can refer to the same office, but the first is less admiring and likely to connote the view of employees lower down in the company—nobody wants to be thought of as “bossy.” Higher executives would be more likely to speak admiringly of a “CEO.”
I often write “insufficiently complex” at the bottom of student papers instead of “simple-minded.” Although they denote essentially the same quality, the connotations of the first are less insulting.