Most Protestants and too many Catholics think that celibate means chaste, it doesn't. I simply means that priests take a vow to not marry so that their number one priority is to the Church and its flock, not to their personal family. Sexual activity out of wedlock is a sin for priests no different than for any other Catholic.
Um, while celibacy and chastity are different, celibacy includes chastity. Celibacy includes renouncing both marriage and sex (including sexual thoughts).
A married person who has sex with his or her spouse is chaste, but not celibate. An unmarried person (e.g., priest) who has sex with anyone is neither chaste nor celibate.