Dominance basically refers to some form of power over others established through intimidation.
Rank means a relative position in a row, line or series. Individuals may be ranked according to a myriad of criteria. Status is often a more general term meaning a state, condition or position, which is not always a relative population, in a ranked order. Hierarchy is a group of things which are arranged in order of rank or grade according to some value system or set of criteria. A linear hierarchy reflects a straight line rand ordering of animals usually created by dominance.