Final answer:
The genitofemoral nerve pierces and travels down the Psoas Major muscle before dividing into genital and femoral branches. This nerve is distinct from the sciatic nerve, which originates from the sacral plexus and travels to the posterior leg.
Step-by-step explanation:
The nerve that pierces the Psoas Major muscle and then travels down inferiorly on its surface before dividing into two branches is the genitofemoral nerve. This nerve starts from the lumbar plexus within the Psoas Major muscle and courses inferiorly on the anterior surface of the muscle. It eventually splits into two branches, the genital and the femoral branches, which serve different physiological functions by supplying the genital region and the anterior upper thigh, respectively. This nerve is different from the sciatic nerve, which is a systemic nerve from the sacral plexus and is a combination of the tibial and fibular nerves. It extends across the hip joint and gluteal region into the upper posterior leg.