For maximum mechanical efficiency in a squat the weight of the bar needs to be aligned with the middle of the lifter’s foot. When the bar travels either side of the vertical line it creates an unnecessary lever arm resulting in a mechanical disadvantage.
This means that the placement/positioning of the bar in a squat will determine the mechanics and muscular involvement of the lift. Each different position of the bar requires a different positioning of the torso if we are to maintain this bar/mid-foot relationship.
In a front squat the bar is racked on the deltoids (across the front of the shoulders), so in order to maintain the bar/mid-foot alignment the torso will remain very vertical. This shift in torso positioning results in an acute knee angle. This places more emphasis on the quadriceps and glutes as the primary movers. There’s essentially no hamstring involvement out of the ‘hole’ (bottom of the squat) or during the rise of the squat because the hamstrings are already fully contracted and slack so they cannot be contracted to help extend the hip out of the hole.
There are two versions of back squats, the high-bar or Olympic back squat and the low-bar or powerlifters back squat.
In an Olympic back squat the bar is placed on top of the traps. This shift means that the torso also needs to shifts, with a slight inclination forward. The movement of the Olympic squat is very similar to that of the front squat a “drop down and stand up” approach. Again this style of squat is more quadriceps dominant but due to the slight forward lean the hip and knee angles allow for some hamstring tension. During the upper portion of the squat the hamstrings can assist to maintain the back angle.
In the low-bar or powerlifting squat the bar is placed across the rear deltoids (along the spine of the scapular). Again the torso lean increases. The emphasis is now placed on the posterior chain and ‘hip drive’ movement and wanting to create a stretch reflex to “bounce” out of the hole. The stretch reflex is created because the hamstrings remaining under tension throughout the eccentric movement. Knee positioning becomes more important in a low-bar squat because of the knees shift too far forward then hamstring tension will lessen and the stretch reflex will be lost.
In conclusion the different squatting styles will place emphasis on different musculature, so understanding this means you can best chose which squats suit you best for what you wish to train.