Open-water diving has at least two different meanings in SCUBA diving:
in the later stages of initial diver training, divers progress from diving in swimming pools to open water, where open water normally means the sea or a lake
any diving where the surface of the water immediately above the diver is in contact with the earth's atmosphere. Open water diving implies that if a problem arises, the diver can directly ascend, vertically to the atmosphere to breathe air. So, penetration diving involving entering caves or wrecks or diving under ice is not "open water"" diving.
