The squat that involves lowering a barbell onto the back of the shoulders is the back squat. In this exercise, the bar rests across the upper back or trapezius area while the lifter bends the hips and knees, lowers the body, and then stands again.
Back squats are a foundational strength exercise because they train the quadriceps, gluteus maximus, adductors, and supporting trunk muscles. The bar can be placed relatively high on the upper trapezius, producing a high-bar squat, or lower across the upper back and rear deltoids, producing a low-bar squat. These are both forms of the back squat, not separate answers to the question.
The front squat is the most common mix-up: its bar rests in front of the body across the clavicles and front shoulders. An overhead squat holds the bar above the head, while a goblet squat uses a dumbbell or kettlebell held in front of the chest. None places the bar on the back of the shoulders.
The back squat is also one of powerlifting’s three competition lifts, alongside the bench press and deadlift. Depth, stance, bar position, and equipment can vary by training style and ruleset.