I know that the various devotions began, for the most part, in a time when information was very hard to communicate between geographically-distant areas or between cultures that spoke different languages. Mary, Star of the Sea would have been familiar in Latin America for decades before it became popular in Italy, and Our Lady of the Snows is a devotion not commonly found outside of Italy and the Midwest US (where there is a Shrine devoted to this apparition). It strikes me that one could be devoted to Mary in any sense, but that since devotion is by its nature a very personal calling, it’s not unlikely that one is called to a particular devotion.
There are some such devotions to the Lord Jesus Christ. One is Infant Jesus of Prague, which was brought to the U.S. by Czech (or ethnically Slav) immigrants and has a profound cultural meaning - during one of the many wars between Muslims and Christians in southeastern Europe, a child was seen giving out food in what was essentially a prison camp by occupying Muslims for impounding Christians. That child was believed to be related to a prior apparition of the Infant Jesus, who was seen in Prague. There are prayers directed towars Christ in the Nativity, Christ on the Cross, Christ in Gethsemane, Christ in the Desert, etc.
What is interesting is that, for all the varied history of devotions, the tendency is towards a handful - the Rosary, the Immaculate Hearts, St. Francis, St. Therese of Liseaux. Despite the prominent roles and volume of writings left by them, few keep a devotion to St. Paul the Evangelist, St. Thomas Aquinas, St. Irenaeus of Smyrna, etc.
I personally keep a devotion to the Holy Trinity.