Do all types of Priests make a vow of celibacy?
No. Priestly celibacy is practised in the Latin rite, but there are Eastern Catholic rites which still have married priests. Priestly celibacy is not a doctrine but a discipline
There are also some Anglican and Episcopalian priests who converted to Catholicism and have been ordained priests in the Catholic Church who are married.
No, only religious priests make vows. Secular (diocesan) priests make promises instead.
getting close: The Eastern Rites will ordain a married man. NOTE the marriage comes first. Only an unmarried man (widowers count!) may become a Bishop.
In the Latin Rite:
A diocesan priest makes a promise not to marry, i.e., remain celibate. “Celibacy” is simply the state on not being married. Thus a diocesan priest simply breaks a promise if he marries - and incurs whatever penalties apply. If he engages in sex outside marriage, it is a sin like any one else, but it does not break his promise since he has not married.
A regular priest (one in orders who follows a rule - regular means rule - e.g., a Benedictine, etc.) takes a vow of chastity as a celibate. If he were to marry it would break his vow. Similarly, since any sexual activity outside marriage in unchaste, he, in addition to the sin, breaks his vow.
Dispensations are just that…
Getting even closer: Benedictines do not vow chastity.
The three Benedictines vows are stability, obeidence to the rule of life and to the abbot, and ongoing conversion. Celibacy is implied in the vow of obedience, but it is not a vow in-and-of itself for Benedictines.
Incidentally, Benedictines don’t practice poverty either. Not too long ago, St. Vincent Archabbey in LaTrobe Pennsylvania was the largest land owner in the state. Brother Micheal at the Cistercian Monastery of Our Lady of the Holy Spirit in Conyers, Georgia said to me, “Are you kidding? I am co-owner of two factories and twenty two hundred acres in Suburban Atlanta. I’m pretty rich.”
Learn something new every day