Resent is what the person who is offended often feels.
If I resent something, I am annoyed or even angry at it, often with a feeling of injustice or having been wronged.
"Alice had offended Sue at the party with a comment about how ridiculous she looked. Sue resented it, so much so that she left."
In the passive sense, a person may feel offended.
A person who feels offended may often resent it, but no always. I may feel offended if a person uses foul language, but I may not resent it.