Masseter Muscle Spasm: This condition is characterized by the spasm of the masseter muscle, which is one of the muscles of mastication. The location of the spasm, at the point where the mandible meets the upper jaw, is consistent with the masseter muscle's anatomy. The "pop" sound could be due to the sudden release of tension in the muscle.

Medial Pterygoid Muscle Spasm: Similar to the masseter muscle, the medial pterygoid muscle is another muscle of mastication that could cause jaw pain and spasm. Its location is also near the point where the mandible meets the upper jaw.
Myofascial Pain Syndrome: This condition is characterized by pain and inflammation of the muscles and their surrounding connective tissue. It could cause chronic jaw muscle spasm and pain.
Bruxism: This condition involves grinding or clenching of the teeth, which could lead to jaw muscle spasm and pain.

Trigeminal Neuralgia: Although less likely, this condition involves sudden, severe facial pain and could be triggered by muscle spasm. It is essential to rule out this condition due to its potential for severe pain and impact on quality of life.
Dental Abscess or Infection: An abscess or infection in the teeth or gums could cause referred pain to the jaw and face, leading to muscle spasm.

Hemifacial Spasm: A rare condition characterized by involuntary muscle spasms on one side of the face, including the jaw.
Eagle Syndrome: A rare condition where an elongated styloid process or calcified stylohyoid ligament causes pain and discomfort in the jaw and face.
Temporomandibular Joint (TMJ) Disorder with Referred Pain: Although the question states that the pain is not at the TMJ joint, it is possible that a TMJ disorder could cause referred pain to the area where the mandible meets the upper jaw.