The term "rosary" used as a proper noun, Rosary, designates the well-known Dominican rosary. All other arrangements of beads are properly called chaplets or crowns, or simply beads. But in popular writings and among the faithful these chaplets are called rosaries as well.
All the faithful are acquainted with the Rosary of the Blessed Virgin Mary. The entire Rosary contains fifteen decades until the recent time when Saint John Paul II, while Pope - added another five and called it The Luminous Mysteries. The one more commonly used is that with five decades, a third part of the whole. This is the well-known Dominican Rosary. Originally the name Rosary was used to designate the entire twenty decades, whereas the five decade one was called corona (crown). This distinction, however, is no longer observed, and these names are used synonymously.
Many Catholics are acquainted with one or more of the other types of rosaries or chaplets which have come into use in the course of time. Many of these are more or less connected with a certain religious order, which furthers a particular form of devotion. Thus, besides the ordinary Dominican rosary, there is the Franciscan Crown and St. Anthony's Chaplet (Franciscans), Brigittine Rosary (Brigittines), Crosier Beads (Crosier Fathers), Chaplet of the Five Wounds (Passionists), Crown of our Lord (Camaldoles), Chaplet in honor of the Precious Blood (Precious Blood Fathers), Rosary of the Seven Sorrows (Servite Fathers) among many others.
It is interesting to note that nearly every type of rosary has a different number or arrangement of beads. Thus the complete Dominican Rosary has 20 decades, the Franciscan Crown has 7 decades, the Brigittine has 6 decades, the Crosier has 5 decades, the rosary for the dead has 4 decades, the Crown of Our Lord has 3 decades. The Chaplet of the Seven Sorrows has 7 groups of 7 beads, that of the Holy Ghost has 5 groups of 7, as also that of the Immaculate Heart of Mary; the chaplet of the Holy Face has 5 groups of 6, that of the Precious Blood has 6 groups of 5; that of the Five Wounds has 5 groups of 5, as also the Sacred Heart. St. Anne's has 3 groups of 5. The Chaplet of Immaculate Conception has 3 groups of 4; that of St. Joseph and the Way of the Cross-have 15 groups of 3 while St Anthony's has 13 groups of 3; the Angelic Crown has 9 groups of 3. The beads of the Blessed Sacrament numbers 33, of St. Philomena numbers 13 and 3 while that of the Infant of Prague numbers 12 and 3.
Usually no special color is prescribed for the beads of the various chaplets. But in that of St. Joseph there are white and blue beads, symbolizing his purity and piety. Another case is that of the Crown of St. Philomena, in which the beads must be white and red. The beads of the Chaplet of the Precious Blood are red, as also those of the Crown of Our Lord and of the Sacred Heart.
I hope that this information has given you a glimpse of how rich these devotions are. May the Blessed Mother, Queen of the Most Holy Rosary continue to inspires us to deepen our life of prayer and devotion as an expression of our love for God.
___notes; from TWENTY-FOUR ROSARIES AND CHAPLETS 1994.