Tonnage was originally the tax on tuns (casks) of wine shipped to England, mostly from Spain and Portugal, under a subsidy granted to the English crown by Parliament starting in the Fourteenth Century. Today, in maritime use, tonnage varies in meaning depending on the vessel. It can refer to the weight of a loaded or empty vessel, or to its volume or its cargo volume. Measurement of tonnage can be less than straightforward, not least because it's used to assess fees on commercial shipping. Port authorities, naval architects, and owners may have different approaches to calculating it.
Gross Tonnage or Gross Register Tonnage is the internal volume of a vessel plus the space on exposed cargo decks (with some exemptions, depending on the assessing body). It (or Net Tonnage, below) is used for calculating canal transit or harbor fees, and is often expressed in gross tons, measurement tons, or cubic meters.
Net Tonnage or Net Register Tonnage is Gross Tonnage less the volume of spaces that will not hold cargo (engine compartment, helm station, crew spaces, and so on, again with differences depending on which port or country is doing the calculations). It represents the volume of the ship available for transporting freight or passengers. Register Tonnage calculations are complex. A hold can for instance be assessed for grain (all the air space in the hold) or for bales (exempting the spaces between structural frames). Net Tonnage is often expressed in gross tons, measurement tons, or cubic meters.
Displacement Tonnage is the actual weight of the vessel and its contents. It's often used to rate naval vessels, since their weight is fairly constant and they're not subject to the kinds of port fees that are calculated on Register Tonnage. It's often expressed in long tons or in metric tons.
Deadweight Tonnage is the maximum weight of the vessel's contents (its carrying capacity). It includes the crew, passengers, cargo, fuel, water, and stores. Like Displacement Tonnage, it's often expressed in long tons or in metric tons.
A Measurement Ton measures space. It equals 100 cubic feet.
A Freight Ton also measures space. It equals 40 cubic feet.
A Long Ton measures weight. It equals 2,240 pounds.
A Metric Ton measures weight. It equals 1,000 kilograms. (Technically, a gram measures mass, but in this context it is treated as measuring weight.)
It's not hard to estimate a ship's actual weight (displacement tonnage). Estimate how many cubic feet of water it's displacing (the volume of the hull lying below the water). Multiply by 64 (the weight of one cubic foot of seawater) to get an estimate of the weight of the ship in pounds.