What is the difference between a CHECK CONSTRAINT and error handling?

A CHECK CONSTRAINT will automatically throw an error in response to the insertion of invalid data.

TRY + CATCH can be used to handle (ie: suppress and programmaticaly respond to) an error.

THROW | RAISERROR can be used to programmatically raise an error.

BTW: This type of "explain the difference between" question is good for asking candidates during intermediate level interviews.