Priority, precedence can both mean the act, the fact, or, especially, the right of preceding another.
When the reference is to the right, both terms usually imply an established or accepted code that determines which shall precede the other.
Priority is the usual term in law and the sciences and chiefly concerns an order of time. When there is merely a question concerning the time relations of events, the term implies antecedence in occurrence.
When, however, the question concerns a number of things (as debts or cases) which cannot be taken care of or dealt with all at once and must be arranged in order of time, priority suggests a rule of arrangement that determines the order in which one goes before another.
Precedence, though frequent in general use, is, in the sense under consideration, primarily a term of formal etiquette; it then implies an established order (as in receiving, greeting, or seating) which gives preference to those who are superior in rank, dignity, or position.
In more general use the term often suggests a prior place, chance, or seat accorded to one, often because of age, sex, social position, or as a mere courtesy.