When I was in the seminary with the Dominican Order, I learned that they have a tradition of saying the Rosary that is slightly different than what most Catholics do. (We called the latter the “Roman” Rosary, but I don’t know if it is its “official” name.) The Dominican version begins by making the Sign of the Cross while saying the first half of the Hail Mary, then the verse/response for the beginning of the Divine Office, and finally the Glory be.
Leader: Hail Mary, full of grace, the Lord is with thee.
Response: Blessed art thou amongst women, and blessed is the fruit of thy womb, Jesus.
L: O Lord, open my lips.
R: And my mouth will declare your praise.
L: O God, come to my assistance.
R: O Lord, make haste to help me.
L: Glory be . . .
R: As it was . . .
Then the leader announces the first mystery. What is also slightly different is that the leader and group/congregation alternate parts thoughout the Rosary: the leader says the first part of the Our Father’s, Hail Mary’s and Glory be’s for the first, third and fifth mysteries, while the group says the first parts of the prayers for the second and fourth mysteries. The Dominican Rosary ends with the same prayers. I still pray the Rosary this way by myself.
Someone once offered the explanation for the different tradition by saying that it was shorter, and we Dominicans had to get back to our study and preaching, but I doubt that was the real reason. More likely, this tradition of saying the Rosary is older and so simpler, and has monastic elements. The “Roman” Rosary added the other prayers at the beginning over the course of time.
Other religious orders do have their own “chaplets” which may be variations of the Rosary, or entirely different sets of prayers and meditations. The Franciscans have theirs (though I don’t know much about it) and the Servites have a chaplet with (I believe) seven sets of seven beads on which they meditate on the seven sorrows of Our Lady.
