The term 'BEGS TO DIFFER' is an idiom that means to disagree with someone. It is often used when someone has a different opinion or point of view than another person. The crossword solution for this term is 'DISSENTS', which means to express disagreement or disapproval. Therefore, the term 'BEGS TO DIFFER' and the crossword solution 'DISSENTS' both refer to expressing disagreement or disapproval.