We are hitting all around the answer. I agree with Mr. Romig that the terminology is most likely a marketing strategy.
Mr. Day also brings up a great point in that we now must factor in the single barrel trap gun. So how would Parker market its products/ keep up with the competition/ etc offer a gun for skeet, double trap, american (singles) trap.
The name just designates some features. Certainly does not define what one would need or have to have to compete. (look how the guns/ features changed from 1890's to 1920's, etc. Compare to todays o/u's. Everyone wants these tall ribs for "upright posture". Always a fade or new thing to continue to sell products)
As far as the beavertail fore end goes. They were being fitted/ made much earlier than they were cataloged. I have one that letters correct in 1917. (the gun was certainly used for doubles trap, she has provenance to prove such. 34" barrels, raised solid rib, no saftey, large fore end, pistol grip, monte carlo stock, specific chokes in each tube, 2 7/8" chambers, lots of special requests on this gun)
The repeating theme for Parkers is you cant say never/ no way. They always seem to suprise us.