Just remember, radiation efficiency is defined (at least by IEEE) as "The ratio of the total power radiated by an antenna to the net power accepted by the antenna from the connected transmitter."  Thus, it is JUST the internal losses of the antenna, although you'll commonly see it used somewhat interchangeably with the total efficiency, which includes the VSWR term.  Total efficiency is radiated output (TRP) / cabled input forward power.  The net power into the antenna is reduced from the forward power by the reflectivity/mismatch at the antenna which rejects a (often large) portion of the energy back to the source.  It's this VSWR/matching term that is usually the bigger loss component of an antenna design than is the internal resistive losses of the antenna.  Very rarely do antenna designers worry too much about the radiation efficiency, unless maybe they're trying to increase bandwidth by using lossy elements.  

And in case you care, remember that gain is directivity plus (total) efficiency in dB. 

Agree with Michael Foegelle