What is the difference between a tank and vessel?

A tank is designed to hold the maximum hydrostatic pressure at the base -- based on the depth of the tank, the density of the material it holds, and maximum atmospheric pressure (with added margin for safety). A tank wall may be constructed with 'thicker' material at the base and 'thinner' material at the top, to save cost. The top of the tank need only support its own weight (plus safety margin).

A pressure vessel must withstand the rated pressure at all points around the surface of the vessel.