The best way to answer this question is to say that laws in a unitary system are made and implemented from the top down while laws in a federal system can be made and implemented in a more decentralized way.
In a unitary system, the national government has essentially all of the power. It tells the lower levels of government what they can and cannot do. Laws are created by the national government, not by the lower levels of government. The national government tells the lower levels of government how to implement the laws. This is all very top-down.
In a federal system, things can be more decentralized. Of course, the national government still has the power to make laws. However, the states (or provinces, or whatever the lower levels of government are called) also have the independent power to make laws. The states are not simply limited to implementing laws that the national government makes. When the national government does make laws, the laws may at times be implemented in a more decentralized way. The lower levels of government may be able to have some amount of say in how the laws are carried out.
Overall, the national government has much more power in a unitary system than it has in a federal system. This means that the laws in a unitary system are generally made and carried out in a much more centralized way in a federal system.