The official standard for diver’s watches is ISO 6425. To pass this standard a watch must pass a series of rigorous tests. However, testing is voluntary and not all companies submit their dive watches to tests that are conducted by an outside agency or companies such as Rolex and Omega, for instance, test in-house. (There’s no ISO testing organization, they just set the standards).
Generally speaking, a watch must be water-resistant to 100 meters minimum. They must also feature a time controller and comply with standards provided by NIHS 92-11 in regard to luminosity, shock resistance, anti-magnetism, and band solidity. Each watch needs to meet 125% of the stated water resistance rating.
Crucially, the watch needs to have an indication that it’s running, such as a sweeping seconds hand, and it needs to have a luminous element such as a lume on the tip, in order to know it’s running even in dark water. Source: Wikipedia.
If a watch meets the requirements of the tests it can be marked “Diver’s” along with the depth rating. Although, even if a watch does pass the tests, it does not have to be marked as “Diver’s.” This is a term Rolex and Omega both omit despite being leaders in the field of diving watches. (The full array ISO 6425 of tests can be found here.)