Contract and Shrink have the same dictionary definition, however we tend to use shrink when something stays the same overall shape but gets smaller. E.g. "My trousers shrunk in the wash". Contract is generally used like you said, as the opposite of expand. Contract tends to mean to get smaller and tighter. Muscles contract i.e they get smaller and tighter when you exercise them.

First, "expand" is a verb. So the opposite verbs are "shrink" and "contract." The past of shrink is "shrank" and the past of contract is "contracted." Shrink usually means a physical object gets smaller in size. If you wash blue jeans in hot water, they will shrink. My grandmother used to be tall, but in the last few years she shrank by a few inches. Contract has a lot of meanings and it is more common when you are talking about abstract things or concepts, or in formal and academic situations. The economy contracts, for example.