Differ, vary, disagree, dissent mean to be unlike or out of harmony.
Differ stresses the fact of unlikeness in kind or nature or in opinion but does not indicate except through the context the extent or degree of divergence.
Vary (see also CHANGE) though often interchangeable with differ may call attention to readily apparent differences and sometimes suggests a range of differences. The term commonly introduces a statement of the points, the ways, or the degree in which the things or the persons under discussion differ.
Disagree emphasizes lack of agreement and not only may imply differences between things or variance between persons or opinions, but often may suggest incompatibility, unfitness, or disharmony.
Of the words here compared only disagree is used in reference to lack of harmony between a thing and a person that results in mental or physical disorder of the latter.
Dissent denotes a difference in opinion between persons or groups; it may imply refusal to assent to or the withholding of consent from something that is proposed or offered or it may imply the expression of a difference in opinion from a person or persons holding an opposite view.