Trooper (abbr. Tpr) from the French "troupier" is the equivalent rank to private in a regiment with a cavalry tradition in the British Army and many other Commonwealth armies, including those of Australia, Canada, South Africa and New Zealand. Today, most cavalry units operate in the armoured role, equipped with tanks or other armoured fighting vehicles. Some armoured regiments without a cavalry tradition do not use the rank, a notable exception being the British Royal Tank Regiment which follows the naming conventions of its fellow regiments in the Royal Armoured Corps. Cavalry units are organized into squadrons, further divided into troops, hence a trooper is a member of a troop. "Trooper" can also be used colloquially to mean any cavalry soldier (although not usually an officer).
In the British Army, trooper is also used as a rank in the Special Air Service and Honourable Artillery Company. Airtrooper (Atpr) is used in the Army Air Corps.
In the United States cavalry and airborne, "trooper" is a colloquialism that has traditionally been used not as a rank, but rather as a general term for any enlisted soldier.
Cavalry Troopers are generally considered to be socially a cut above other soldiers. This distinction stems from the days when cavalry needed to supply their own mounts, tack etc. In order to supply the mounts and tack the Trooper would need to be reasonably wealthy so the average Trooper was a gentleman of sorts. In addition cavalry regiments were seen to be relatively fashionable and dashing, often having colourful or even garish uniforms.
This historically superior social position is humorously referenced today in the Australian Army, where cavalry Troopers jokingly define their role as: "The role of the Cavalry is to add colour, dash and daring, to what would otherwise be a mindless shitfight amongst grunts". In the British Army the equivalent phrase is "adding tone to what would otherwise be just a vulgar brawl". Both come from a quote by Frederick the Great: "Artillery adds dignity to what would otherwise be a vulgar brawl."