Are a gyrodyne and a compound helicopter the same thing?
I have now found a couple of pretty authoritative definitions for a gyroplane:


FAA Rotorcraft Flying handbook: For Gyroplane Use Only:



  "The 'gyrodyne' is a hybrid rotorcraft that is capable of hovering and yet cruises in autorotation. The first successful example of this type of aircraft was the British Fairy Rotodyne, certificated
  to the Transport Category in 1958. During the 1960s
  and 1970s, the popularity of gyroplanes increased with
  the certification of the McCulloch J-2 and Umbaugh.
  The latter becoming the Air &amp; Space 18A."



Electronic Code of Federal Regulations (e-CFR) Title 14. Aeronautics and Space Chapter I. FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION Subchapter A. DEFINITIONS AND GENERAL REQUIREMENTS Part 1. DEFINITIONS AND ABBREVIATIONS, Section 1.1. General Legal Information Institute, Cornell Law School.



  "Gyrodyne means a rotorcraft whose rotors are normally engine-driven for takeoff, hovering, and landing, and for forward flight through part of its speed range, and whose means of propulsion, consisting usually of conventional propellers, is independent of the rotor system."


So it may be that the gyrodyne fully offloads the rotor and relies on autorotation during cruise, while the compound helicopter drives its rotor throughout. But I can find no authoritative definition of a compound helicopter.

Technically, under autorotation the rotor disc tilts backwards and air flows up and over the blades from below, while under powered drive the rotor disc tilts forwards and the blades drive air downwards from above. It would be nice to think that this was reflected in the two definitions, but there are obviously borderline cases where the disc angle and loading are not quite textbook.