Criminal and civil law. There are two kinds of law in Canada. Criminal law deals with crime, like robbing a bank. A person may go to jail if he or she is convicted of committing a crime. The Crown prosecutor is a lawyer for the government.here are different levels and types of courts in Canada. Each court has a different “jurisdiction”, which means that they can decide different types of cases. There are: 1  Provincial and territorial courts. 2  Superior courts.