late 14c., "be unlike, dissimilar, distinct, or various," from Old French differer (14c.) and directly from Latin differre "to set apart, differ," from assimilated form of dis- "apart, away from" (see dis-) + ferre "to bear, carry," from PIE root *bher- (1) "to carry." Meaning "disagree, be of contrary opinion" is from 1560s.
Two senses that were present in Latin have gone separate ways in English in sense and spelling (probably based on different stress) since c. 1500, with defer (transitive) taking one set of meanings and differ (intransitive) the rest. Related: Differed; differing.