They both may be correct. The bursitis causes pain, you stop moving your shoulder, and develope what is known as a secondary frozen shoulder. Before this improves, the cause of pain must be eliminated first. A primary frozen shoulder forms for no specific reason, and is insidious in its onset. with increasing loss of motion that sometimes goes unnoticed by the patient for some time. Either way, it can some times take a year, before the patient regains full motion.
A related discussion, shoulder and neck pain was started.