Rotator Cuff Tendinopathy or Tear: The patient's presentation of sudden onset sharp pain at the shoulder joint with an aching sensation radiating down the arm, exacerbated by certain shoulder positions and rapid movements, is highly suggestive of rotator cuff tendinopathy or a tear. The limited active internal rotation and shoulder abduction, along with the inability to move the hand off the back on external rotation against resistance, further support this diagnosis.

Subacromial Bursitis: The patient's pain pattern and exacerbation with rapid movements could also be consistent with subacromial bursitis. This condition involves inflammation of the bursa that cushions the rotator cuff tendons, leading to pain and limited mobility.
Early Stages of Adhesive Capsulitis (Frozen Shoulder): Although the patient has a full range of motion in the neck and no significant tenderness on palpation, the limited active internal rotation and shoulder abduction could be early signs of adhesive capsulitis. The pain at night and with certain movements also fits this diagnosis.

Thoracic Outlet Syndrome: Although less likely, thoracic outlet syndrome could present with shoulder and arm pain, especially if there is compression of the nerves or blood vessels in the thoracic outlet. Missing this diagnosis could lead to prolonged pain and potential neurological or vascular complications.
Referred Pain from Cardiac or Pulmonary Issues: Given the patient's history of smoking, it's crucial not to miss cardiac or pulmonary issues that could refer pain to the shoulder. Conditions like myocardial infarction or pulmonary embolism can present atypically, especially in women or diabetic patients, and are medical emergencies.
Infection or Septic Arthritis: Although the patient does not have fever or significant swelling, infection or septic arthritis of the shoulder joint is a serious condition that requires prompt diagnosis and treatment to avoid joint destruction.

Tumors (Bone or Soft Tissue): Tumors affecting the shoulder region, such as osteosarcoma or soft tissue sarcomas, are rare but could present with pain and limited mobility. A thorough examination and possibly imaging studies are necessary to rule out these conditions.
Neurological Conditions (e.g., Brachial Plexopathy): Certain neurological conditions affecting the brachial plexus could lead to shoulder and arm pain, along with weakness or sensory changes. These conditions are less common but should be considered in the differential diagnosis, especially if there are neurological symptoms or signs.