Labrum comes directly from a word Latin for lip, labrum. The two ball-and-socket joints, the hip and the shoulder, each have a labrum: The glenoid labrum surrounds of the rim of the glenoid cavity in the shoulder and the acetabulular labrum surrounds the rim of the acetabulum in the hip. Both labia are composed of fibrocartilage and serve to deepen the sockets of their respective joints thus providing additional stability. The glenoid labrum plays the more important role of the two given the shallow form of the glenoid cavity as compared to the acetabulum.
Glenoid labrum tears are common athletic injuries , especially those sports involving overhand motions such as baseball and tennis.
Labium, directly from Latin word for the curved edge of a cup, labium, is used exclusively for the labium majus and labium minus (plural labia majora and labia minora) of the vulva.
The labrum, here labeled as the glenoid ligament. From Grey's Anatomy, 1909, via Wikipedia.com