The Mossberg 590 Shockwave is classified as a “Pistol Grip Firearm.” That is how it should be entered into your A&D Record and recorded on the 4473.
It is neither a long-gun nor a handgun. Only long-guns can be sold to those under 21 years old so this firearm can not be sold to anyone under 21 years old.
A Henry Lever Action Axe should also be acquired as a “Pistol Grip Firearm” into your A&D record.
An FFL newsletter article titled Recording Pistol Grip Firearms in the Acquisition and Disposition Record (March 2013 Volume 2 page 4) addresses the issue of recording pistol grip firearms in the acquisition and disposition record.
Another FFL newsletter article titled Pistol Grips and Shotguns (November 2009 page 2) states: “Other questions raised pertain to entries made in the licensee’s required records with respect to firearm “type.” These entries should indicate the firearm type as “pistol grip firearm”.”