There are several factors to address when talking about the differences between the front and back squat. The most significant being the bar position on the body and therefore the load on the body. This is what differentiates everything about the two movements. The load changes the mechanics and thereby the muscles used by the body during the squatting movements.
The back squat is one of the most fundamental exercises in strength and conditioning. Whether we are discussing the high bar or low bar back squat (variations of the same movement), the fact remains that the load is supported across the upper back. During the front squat the bar is positioned across the front of the body – typically resting on the deltoids/shoulders, just on or in front of the clavicle. The body position is more upright throughout the movement, as a result of the shift in bar position and the lifters center of gravity. With both movements, hip and thoracic (upper back) mobility/flexibility are important to maintaining proper form and achieve a full range of motion. Developing proper position in both variations of the squat takes time and good coaching, so this is a process that should not be hurried – with regard to both range of motion and load – patience is important for long term health and performance.
The execution of the front squat can be more complex because of the bar positioning, but very beneficial. With this frontal load, the arms/shoulders/thoracic spine and hips must be capable of achieving proper positions of support, which can take time to develop, but is also why it can be such an important movement to learn – as it is a highly transferable movement, i.e. clean, push-press, jerk, etc. It also gives the lifter more control over the bar and load throughout the range of motion – more control means less potential for injury.
Overall the front squat requires more effort to complete, recruiting more muscle, and ultimately burning more calories. So, if your not including the front squat in your strength and conditioning program, ask your trainer/coach to guide you through the learning process and build a stronger foundation while burning more calories.