**Core Concept**
The development of the face and neck is closely linked to the pharyngeal arches, each of which gives rise to specific muscles, bones, and arteries. The third pharyngeal arch is a crucial developmental structure that contributes to the formation of various cranial and neck muscles.

**Why the Correct Answer is Right**
The muscle of the third pharyngeal arch is primarily the stylopharyngeus muscle. This muscle originates from the stylopharyngeus bone and inserts into the pharynx, playing a key role in the swallowing process. The stylopharyngeus muscle is innervated by the glossopharyngeal nerve (cranial nerve IX), which carries both sensory and motor fibers.

**Why Each Wrong Option is Incorrect**
**Option A:** The digastric muscle is primarily associated with the first pharyngeal arch.
**Option B:** The sternocleidomastoid muscle is a derivative of the second pharyngeal arch.

**Clinical Pearl / High-Yield Fact**
The pharyngeal arches are essential in understanding the embryological development of the head and neck region. Recognizing the muscles associated with each arch is crucial for identifying the innervation patterns and clinical correlations.

**Correct Answer:** C. Stylopharyngeus muscle.