What is the difference between the state and federal governments?

Simply put:

Government: Their laws encompass all of the United States and minor outlaying territories.

State: Their laws only cover the boarder of their particular states.

A popular example of this in action is:

Medical Marijuana is recognized by STATE law in California and other "green" states. Thus shops can legally open up in counties that allow it. State paid police cannot unjustly raid and close a Marijuana clinic. (County sheriff's and local)

Medical Marijuana is not recognized by FEDERAL law. Thus the Federally paid police (Drug Enforcement Administration) can raid these clinics legally. (and often jointly with sheriff dept)

Additional Information:

Local (county sheriff for example) police are under ANOTHER set of laws not enforced by State or Federal.