**Core Concept**
Parathyroid carcinoma is a rare and aggressive malignancy of the parathyroid glands, characterized by uncontrolled cell growth and invasion. The diagnostic features of parathyroid carcinoma are crucial for distinguishing it from benign parathyroid disorders, such as adenomas and hyperplasia.

**Why the Correct Answer is Right**
Parathyroid carcinoma is often diagnosed based on the presence of metastasis to regional lymph nodes or distant sites. This is because parathyroid carcinoma tends to invade adjacent structures and spread through the bloodstream or lymphatic system. The correct answer is related to the metastatic potential of parathyroid carcinoma, which is a key feature that distinguishes it from benign parathyroid disorders.

**Why Each Wrong Option is Incorrect**
**Option A:** Elevated serum calcium levels are a common feature of parathyroid disorders, but they are not specific to carcinoma. Both benign adenomas and hyperplasia can cause hypercalcemia.
**Option B:** Parathyroid hormone-related protein (PTHrP) is a tumor marker associated with parathyroid carcinoma, but it is not the most reliable diagnostic feature.
**Option C:** Parathyroid gland enlargement can be seen in both benign and malignant conditions, making it an unreliable diagnostic feature.

**Clinical Pearl / High-Yield Fact**
When suspecting parathyroid carcinoma, it is essential to evaluate for metastasis to regional lymph nodes or distant sites, as this is a critical feature that distinguishes it from benign parathyroid disorders.

**Correct Answer:** D. Metastasis to regional lymph nodes or distant sites.