Primary Hyperparathyroidism: This condition is characterized by the excessive production of parathyroid hormone (PTH) by one or more parathyroid glands, leading to hypercalcemia (high calcium levels), hypophosphatemia (low serum phosphorus), and increased urinary excretion of phosphorus. The low urine calcium in the context of high serum calcium and high PTH suggests that the kidneys are responding appropriately to the high PTH by increasing calcium reabsorption, which is a hallmark of primary hyperparathyroidism.

Familial Hypocalciuric Hypercalcemia (FHH): This is a genetic disorder that leads to an abnormality in the calcium-sensing receptor of the parathyroid gland and kidney, resulting in hypercalcemia, high PTH levels, and typically low urinary calcium excretion. The clinical presentation can mimic primary hyperparathyroidism but is distinguished by its familial occurrence and the characteristic low urinary calcium excretion.
Lithium-Induced Hyperparathyroidism: Lithium therapy can lead to increased PTH secretion and hypercalcemia. The mechanism involves lithium's effect on the parathyroid gland, increasing its set point for calcium, leading to increased PTH secretion for any given level of serum calcium.

Malignancy-Associated Hypercalcemia: Although malignancy often presents with high calcium and low PTH (due to PTHrP production by tumors), some cases can have elevated PTH levels, especially in the context of paraneoplastic syndromes or direct involvement of the parathyroid glands by metastatic disease. Missing this diagnosis could be fatal due to the underlying cancer.
Vitamin D Intoxication: Excessive intake of vitamin D can lead to hypercalcemia, which in turn can cause secondary hyperparathyroidism. However, the high PTH in this context is usually not as pronounced as in primary hyperparathyroidism. Vitamin D intoxication can also lead to increased renal reabsorption of calcium, potentially resulting in low urine calcium.

Hyperparathyroidism-Jaw Tumor Syndrome: A rare genetic disorder characterized by hyperparathyroidism, jaw tumors, and other abnormalities. It presents with high PTH and calcium levels but is distinguished by its association with jaw tumors and other specific clinical features.
Parathyroid Carcinoma: A rare cause of primary hyperparathyroidism, characterized by a malignant tumor of the parathyroid gland. It can present similarly to benign primary hyperparathyroidism but is distinguished by its potential for local invasion and metastasis.