The similarities and differences between state government and a regime are varied and subtle.
When a large territory is united under one government, yet has divisions of smaller territories within itself, you have the setting for two sets of laws.
In a state, the rules of the law are dictated by the state. As long as they do not go against the rules of the country, they are the laws that are enforced. For example, a federal law may give a person the right to own crayons. The state may set up a controlling law which says that ownership is fine, but you may not use them in a state-owned establishment. The state accepts the federal law but limits it within its own borders.
In a regime, there are still the two sets of laws. The difference being that the larger territory defines the laws of the smaller one. The federal government says, “You may have crayons, and since you are a part of OUR country, you may use them wherever you please.” The smaller division of the country has no power to restrict crayons within areas particular to it.