Resume means "to go on (or take up again) after an interruption." Continue has precisely the same meaning except that no interruption is involved. A group might continue to play bridge, but would resume playing after a stop for refreshments."The rain continued for three hours, stopped for a few minutes, and then resumed." Words related to continue are persist, last, persevere, endure, and extend. Phrases synonymous with resume are "begin again" and "start once more."
Dictionary of problem words and expressions. Harry Shaw. 1975.