"bklyndisp54", from one old guy to another. (I remember those Ward LaFrance -CD rigs too). I first heard of a Rescue Pumper about ten years ago when the Dept I was on, closed down our Rescue Co. We were also in need of buying another Engine, so what they did was buy a "Rescue Pumper". It was a fire truck with a few extra bunker boxes to house a Hurst tool and Air Bags.
I guess the closet comparison of one in the FDNY is the Squad Cos. Back when I was a younger guy, Bridgeport, Ct ran a "Rescue Pumper" for years. It still does. Way back then in the 1950's it just "wasn't" called a "Rescue Pumper". It was just called Squad 5.