Where the non-cognoscenti get confused, is that the Oz Infantry arm is known as the Royal Australian Regiment. Then they see RAAC, RAA, RAE, RASigs, RAEME etc. and assume it goes right across the Army as a whole. Not many of the Reserve units carry the Royal prefix, ISTR.We get the same here in Aus, "Royal Australian Army" is heard now and again, I guess mostly by non-Australians but not always.
With our British Army lineage, we have have a mixture of Royal and non-royal Corps and Regiments also.
But of course most of you knew that anyway!