First you need to define terms. Celebate means not getting married, chaste means not having sex, of course celebate has come to mean both but in Church definitions I think it is still seperate. What a number of seminarians were taught back in the 70s was that you could practice homosexual sex and remain celebate. It was called the 3rd Way or some such thing. I knew a young man who was taught this by a priest. He was brought into the life-style by a priest! I was not sure at the time if the priest was a member of the order he was in formation with or not, and my friend was very careful not to tell me the priest's name. Not long after this he was kicked out of the seminary and years later finally left the Church altogether. Unfortunately, many do not leave when they can't accept the teaching of the Church but stay and try to "reform" the Church.
No. Celibacy is not having sex (and, secondarily, not being married, which is how the homosexuals restrict the definition for it to include them). Thus, children, single adults not having sex, widows and widowers, etc. are celibate. Chastity is maintaining sexual conduct according to one's station in life: celibate if not married, being sexually faithful to one's spouse if married. Thus, one is being perfectly chaste in having sexual relations with one's wife or husband, when that partner is, indeed, the only one. And a person under vows or promises of chastity is both celibate and chaste if unmarried or chaste if married and faithful to the spouse.
Therefore, all celibate people are chaste, but not all chaste people are celibate.