Inherent Authority or Inherent Power?

In the Washington Times:

"'During the Clinton administration, Deputy Attorney General Jamie Gorelick testified before Congress in 1994 that the president has inherent authority under the Constitution to conduct foreign intelligence searches of the private homes of U.S. citizens in the United States without a warrant, and that such warrantless searches are permissible under the Fourth Amendment. "

Can this be true, that Deputy Attorney General Gorelick testified the President thought he had the constitutional power to search private homes of U.S. citizens without a warrant?

And, why are we talking about authority instead of power?

"The Foreign Intelligence Surveillance Act of 1978 also allows eavesdropping without a court warrant so long as it is reported to the FISA Court within 72 hours. When President Carter signed it into law, it was "a presidential concession as to who had the authority," Mr. Specter said. "Congress exercised it by passing the law and the president submitted to it."

Congress has enumerated powers, not enumerated authorities. The President has the executive power, not the executive authority. I don't understand the conceptual idea of Congress "giving authority" to the President.