**Core Concept**
The question is testing the knowledge of the anatomy of the pelvis and the sciatic foramina, specifically the structures that pass through these openings. The greater sciatic foramen is a large opening in the posterior pelvis, while the lesser sciatic foramen is a smaller opening inferior to the greater sciatic foramen.

**Why the Correct Answer is Right**
The piriformis muscle and the sciatic nerve are two structures that pass through the greater sciatic foramen, but not through the lesser sciatic foramen. However, there is another structure that passes through both foramina: the pudendal nerve and internal pudendal vessels. The pudendal nerve originates from the sacral plexus and passes through the greater sciatic foramen, but then re-enters the pelvis through the lesser sciatic foramen to innervate the perineal region. This unique pathway allows the pudendal nerve to supply the muscles and skin of the perineum.

**Why Each Wrong Option is Incorrect**
**Option A:** The sciatic nerve primarily passes through the greater sciatic foramen, but not through the lesser sciatic foramen. It is a major nerve that supplies the lower limb and is not associated with the lesser sciatic foramen.
**Option B:** The piriformis muscle is a significant muscle that passes through the greater sciatic foramen, but not through the lesser sciatic foramen. It is a key muscle in the posterior pelvis and is not related to the lesser sciatic foramen.
**Option C:** The obturator internus muscle passes through the lesser sciatic foramen, but not through the greater sciatic foramen. It is a muscle that helps to stabilize the hip joint and is not associated with the greater sciatic foramen.
**Option D:** The gluteus maximus muscle primarily passes through the greater sciatic foramen, but not through the lesser sciatic foramen. It is a key muscle in the gluteal region and is not related to the lesser sciatic foramen.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the pudendal nerve passes through both the greater and lesser sciatic foramina, making it a unique structure in the pelvis. This knowledge is crucial for surgeons and anesthesiologists when performing procedures in the perineal region.

**Correct Answer:** D. The gluteus maximus muscle primarily passes through the greater sciatic foramen, but not through the lesser sciatic foramen.