BSA marketed these rifle under different names in different countries. The "Royal" was sold in the USA while in Canada the same rifle in long action was marketed as an "Imperial" or "Royal" . So refering to the same rifle as a Royal or a Hunter or an Imperial all depends on point of view. BSA NEVER marked any of their early rifle as to model and the various names seemed to be made up on the fly.
Over the years I have owned several different examples of BSA rifles and the original Mauser clone discontinued ~1959 , regardless of what name you call it, is the best of the bunch by far. My personal favorite was the Royal/Hunter/Imperial featherweight which tipped the scales in long action at around 6 pounds! Not too bad for a wood stocked rifle with a 22" barrel eh?