Piriformis Syndrome: This condition is characterized by pain in the buttocks that radiates down the back of the thigh and into the leg, often due to compression of the sciatic nerve by the piriformis muscle. The symptoms described, including the desire to stretch and the nature of the pain, are consistent with piriformis syndrome.

Sciatica: This involves pain that radiates along the path of the sciatic nerve, which branches from the lower back through the hips and buttocks and down each leg. The pain can be dull and is often accompanied by a feeling of tightness or pressure.
Trochanteric Bursitis: Inflammation of the bursa over the trochanter (a bone on the outside of the hip) can cause pain on the outer aspect of the hip and thigh, which may radiate down towards the knee or ankle, especially when lying on the side or climbing stairs.
Gluteal Strain: A strain in the gluteal muscles can cause pain in the buttocks that may radiate down the thigh, especially with activities that involve the gluteal muscles.

Deep Vein Thrombosis (DVT): Although less likely, DVT can cause pain and swelling in the leg, which might be perceived as tightness or pressure. It's crucial to consider DVT due to its potential for severe complications, such as pulmonary embolism.
Osteonecrosis of the Femoral Head: This condition, also known as avascular necrosis, involves the death of bone tissue due to a lack of blood supply. It can cause hip pain that may radiate down the thigh and is a critical diagnosis not to miss due to its potential for significant morbidity.

Peripheral Artery Disease (PAD): While more common in older adults, PAD can cause pain in the legs when walking (claudication) due to reduced blood flow. The pain typically subsides with rest.
Neoplastic Processes: Tumors, either benign or malignant, in the bone, soft tissue, or nerves can cause a variety of pain patterns, including those described. These are less common but important to consider in the differential diagnosis.