All 4 Uses of

contrary

in

The Winter's Tale

The king hath on him such a countenance As he had lost some province, and a region Lov'd as he loves himself; even now I met him With customary compliment; when he, Wafting his eyes to the contrary, and falling A lip of much contempt, speeds from me; So leaves me to consider what is breeding That changes thus his manners.
Scene 1.2 (definition 1) *

to the contrary = with an opposite or different effect

Hermione, queen to the worthy Leontes, king of Sicilia, thou art here accused and arraigned of high treason, in committing adultery with Polixenes, king of Bohemia; and conspiring with Camillo to take away the life of our sovereign lord the king, thy royal husband: the pretence whereof being by circumstances partly laid open, thou, Hermione, contrary to the faith and allegiance of true subject, didst counsel and aid them, for their better safety, to fly away by night.
Scene 3.2 (definition 2) *

contrary to = in opposition to

My lord should to the heavens be contrary, Oppose against their wills.
Scene 5.1 (definition 3) *

contrary = different (doing something other than what the heavens would dictate)

Definitions:

(1) (to the contrary as in: to the contrary)
with an opposite or different effect; or something with an opposite or different effect

(2) (contrary to as in: contrary to)
in opposition to

editor's notes: You could also think of this as meaning, despite, or in spite of, or in conflict with; but since a common meaning of contrary is opposite, you many find it easiest to think of contrary to as in opposition to.

(3) (contrary as in: a contrary idea)
different (perhaps opposite or mutually exclusive)

editor's notes: In formal logic, contrary propositions or contrary arguments describe two things that cannot both be true. They might be described as mutually exclusive. For example, a pet cannot be both a cat and a dog. It doesn't need to be either, but if it is one, it cannot be the other. So the statement that a pet is a cat and the statement that the same pet is a dog, are contrary statements.