To distinguish or differentiate. These nouns refer to a lack of correspondence or agreement. Difference is the most general: differences in color and size; a difference of degree but not of kind.
From Middle English difference, from Old French difference, from Latin differentia (“difference”), from differēns (“different”), present participle of differre.
Difference, discrepancy, disparity, dissimilarity imply perceivable unlikeness, variation, or diversity. Difference refers to a lack of identity or a degree of unlikeness: a difference of opinion; a difference of six inches.
To tell the difference between two people or things is to see how they are unlike each other. It's hard to tell the difference [= distinguish] between one action movie and another. The new version is supposed to be much better than the old one, but I can't tell the difference (between them).