All 4 Uses

contrary
in
The Winter's Tale
(Auto-generated)

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 *

contrary to = in opposition to
My lord should to the heavens be contrary,
Oppose against their wills.
Scene 5.1 *

contrary = different (doing something other than what the heavens would dictate)
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
I may not, madam; To the contrary I have express commandment.†
Scene 2.2 *

Definitions:

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

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.
(2) (contrary as in: a contrary personality)
disagreeable -- typically in reference to someone's personality
(3) (contrary to as in: contrary to)
in opposition to

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.
(4) (on the contrary as in: on the contrary)
an expression used to intensify denial of an idea
(5) (to the contrary as in: to the contrary)
with an opposite or different effect; or something with an opposite or different effect
(6) (meaning too rare to warrant focus)