If one proposition is the negation of another, it follows trivially from the definition that the two propositions are contradictories. The converse does not hold. Two propositions can be contradictories without either being the negation of the other. For example:
3) John is more than six feet tall
4) John is either exactly six feet tall or else less than six feet tall
are contradictories, but neither is the negation of the other. Negation is one way, but not the only way, of forming a contradictory.