OCD refers to the Discalced Carmelites–the reform initiated by Saints Teresa of Avila and John of the Cross. O.Carm. follow an “unreformed” rule–but it is interpreted variously in different congregations. Both are equally “Carmelite” in their identity and both are part of the larger Carmelite family. There are women and men associated with both.
Many spiritualities and rules have different branches. See, for example, the various types of Benedictines and Franciscans.
I hope this helps.
