In category theory terms the difference between functor and contravariance

is that functor is a structure-preserving mapping between categories: if F is a functor from category C to category D, then F maps objects of C to objects of D and morphisms of C to morphisms of D such that any morphism f:X→Y of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if $h\; =\; g\; \backslash circ\; f$ then $F(h)\; =\; F(g)\; \backslash circ\; F(f)$, and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant while contravariance is a functor which reverses composition.

As nouns the difference between functor and contravariance

is that functor is a function word while contravariance is the reversal of the order of data types acted upon by an operator.