The measurement of vessel tonnage is as old as vessels themselves. It has been a way to tax vessels based on their capacity to carry cargo, and is a measurement of space. Historically, there have been many different systems and those have been subject to many different interpretations by tonnage admeasurers (often the ones with the largest house in port). Gross Tonnage was generally meant to be the amount of space inside a vessel. Net Tonnage was the difference between Gross Tonnage and the Exempted Spaces. Net Tonnage, then, was the space that could be untilized to carry cargo. Besides national tonnage admeasurement, there are also Canal schemes, such as the Panama Canal Tonnage. Again, this is solely for the raising of revenue.
Things like tonnage doors and tonnage floors were used to increase net tonnage by decreasing spaces that could theoretically be used to carry cargo. Tonnage doors supposed to be non water tight (which is why I always get a kick out of seeing a watertight hatch in a tonnage door) to discourage the carriage of cargo in a certain space. Tonnage floors are used to decrease the depth of a space by raising the theoritical bottom, decreasing the potential carrying space.
Think about those older supply vessels. The hatch to the back deck is almost aways in a tonnage door, making the forecastle technically a non watertight enclosure. That is why you see a watertight door on the companionway leading to the engine room tunnel.
The ITC was brought about to supercede the different national admeasurement schemes. It replace the actual measurement of space with a coefficient. It also elimimates the use of tonnage doors, floors or other tricks. This is why a Vessel that has both schemes also has wildly differing tonnage values, between domestic and ITC. I have always felt that licensing would be better based on displacement/horsepower than tonnage.