What is the differences between law and regulation?

The U.S. Geological Survey answers this in a specific context that illustrates the broader concept:

"The difference between laws and regulations are sometimes misunderstood. Congress, and only Congress, enacts laws. Federal executive departments and administrative agencies write regulations to implement the authority of laws. Regulations (as well as Executive Orders and Proclamations) are ancillary or subordinate to laws but both laws and regulations are enforceable. The U.S. Code is the official compilation of codified laws by subject, the U.S. Statutes-at-Large is the official chronologic compilation of all laws, and the Code of Federal Regulations is the official compilation of regulations."

Source: http:/recreation.usgs.gov/env_guide/law.html