The life of celibacy is the state of being unmarried. And yes, we are all celibates.
Chastity is another matter.
This being an inordinately difficult way of life, as we all know too well, the religious binds himself by vow to refrain from the urgings of the flesh. All priests, however and, indeed all human being, are bound by the virtue of chastity. Unfortunately, too many of us fail to dwell on this virtue as often as we should. I hear lots of daily confessions at St. Dominic's in New Orleans. I try to be kind and helpful, failing in that occasionally, to be sure.