Question

How does the constitution delegate powers to the nation differently from how it gives powers to the states?

Answer 1

In constitution the power of the national government is defined clearly. However the power of states is not defined in the constitution. This idea is in line with the idea of federation and limitation of powers : The power that federation have are similar to the national government which allows the states to coordinate but there's a wide room for states to act.

Answer 2

The constitution is the supreme law of the United States and delegates powers to the federal government that supersede the state laws if the two laws differ, individual states have power over laws that don't go against the supreme law.