Not really. You have drop-deck trailers, dump trucks, cube trucks, tow trucks, etc. etc. They are all trucks and trailers. We have the same in the military but we call them Heavy Logistics Vehicles Wheeled, Medium Logistics Vehicle Wheeled, Tank Transporters, Wreckers, etc. They are still just truck and trailers, but we name them after the function they carry.
"Icebreaker" is the same. It is not an indicator of the capacity of the vessel to break through ice. It is an indication of function. Unlike the Coast Guard ones, the AOPS are not there to keep navigation channels open, or to rescue merchant ships stuck in ice, or escort other ships through ice, or generally provide assistance to commercial traffic. Those are the functions of the Coast Guard fleet, thus they are called icebreakers. The GoC has specifically advised commercial shipping that the AOPS will not, repeat, not do that for them in the North and therefore, not to call on them for such purpose. That is why the are not "icebreakers" even though they could act as such.