Courtesy of Professor Darius Rejali of Reed College, author of a history of torture:
This specific water torture, often called the "water cure," admits of several variants:
(a) pumping: filling a stomach with water causes the organs to distend, a sensation compared often with having your organs set on fire from the inside. This was the Tormenta de Toca favored by the Inquisition and featured on your website photo. The French in Algeria called in the tube or tuyau after the hose they forced into the mouth to fill the organs.
(b) choking - as in sticking a head in a barrel. It is a form of near asphyxiation but it also produces the same burning sensation through all the water a prisoner involuntarily ingests. This is the example illustrated in the Battle of Algiers movie, a technique called the sauccisson or the submarine in Latin America. Prisoners describe their chests swelling to the size of barrels at which point a guard would stomp on the stomach forcing the water to move in the opposite direction.
(c) choking - as in attaching a person to a board and dipping the board into water. This was my understanding of what waterboarding was from the initial reports. The use of a board was stylistically most closely associated with the work of a Nazi political interrogator by the name of Ludwig Ramdor who worked at Ravensbruck camp.
Ramdor was tried before the British Military Court Martial at Hamburg (May 1946 to March 1947) on charges for subjecting women to this torture, subjecting another woman to drugs for interrogation, and subjecting a third to starvation and high pressure showers. He was found guilty and executed by the Allies in 1947.
(d) choking - as in forcing someone to lie down, tying them down, then putting a cloth over the mouth, and then choking the prisoner by soaking the cloth. This also forces ingestion of water. It was invented by the Dutch in the East Indies in the 16th century, as a form of torture for English traders.
More recently it was common in the American south, especially in police stations, in the 1920s, as documented in the famous Wickersham Report of the American Bar Association (The Report on Lawlessness in Law Enforcement, 1931), compiling instances of police torture throughout the United States.
Perhaps the main thing to remember here is that all these techniques leave few marks; they're clean tortures and so people who are unfamiliar with them are in genuine doubt as to whether there is much pain. In the absence of a bloody wound, who is to say how much pain there was?
It seems the method that the U.S. has authorized is closest to c), the Nazi one, or d), the one developed by the Dutch and deployed in the American South.
Sure doesn't sound like torture to me.