As a former Armored Cavalry TROOP Commander, allow me to clarify the difference between the terms Troop, Trooper and Troops.

1) Troop: When referring to an Army company sized unit, a Cavalry unit is traditionally referred to as a "Cavalry Troop" (such as A Troop or C Troop, NOT A Company or C Company). Field Artillery and Air Defense Artillery is organized into "Batteries" - all other Army branches are generally organized into "Companies".
2) Trooper: Trooper is an older term of rank used in Cavalry organizations to refer to Cavalry enlisted men in the ranks of Private through Specialist. It is not an "official" rank, but is used more as a term of respect in today's Cavalry and Parachute Infantry organizations to demonstrate the more elite status of the Cavalry or Airborne Soldier versus his peers in less demanding specialties. It is used more in the generic (as in "How many Troopers do you have fit for duty?") than the specific ("Is Trooper Smith fit for duty?").
3. Troops. Troops is a generic, inoffensive catch all term used to refer to military personnel by those not in the military. It encompasses all branches of the service, and is a verbal shorthand for listing total military strength without having to break down the end strength by individual service. For example, it is easier to say "There are 200,000 troops in the Afghanistan Theater of Operations" versus "There are 150,000 Soldiers, 40,000 Marines, 8000 airmen and 2000 sailors in the Afghanistan Theater of Operations.