I have been using the leg press with free weights — not the one on the cables. There are six different foot positions with which I vary my exercise routine. The varying positions activate different parts of the upper leg. Thighs have a major muscle group called quadriceps, which consist of (superior to inferior): rectus femoris, vastus intermedius, vastus lateralis, and vastus medialis.
To aid description of their location, place your hand on your right thigh. The upper part, somewhat laterally, is the rectus femoris. The vastus intermedius is the center of the top. On the lateral edge is the vastus lateralis, then medially is the vastus medialis. All four muscles are depicted in this image that was found on Google and links to DavidDarling.info.
Abductor muscles, used to pull laterally away from midline, are on the lateral edge of your thigh, superior to the quadriceps, closer to your hips. Adductor muscles, used to push medially toward midline, are the inner thigh close to your pelvis.
Standard foot placement is in the middle of the base, shoulder width apart. This is good for your legs overall. Wider foot placement uses more adductors and medial quadriceps. Narrow foot placement activates abductors and lateral quadriceps.
High foot placement activates gluteal muscles and hamstrings. Middle / standard foot placement works quadriceps, hamstrings, and gluteal. Low foot placement activates quadriceps.
This equates to nine variations of foot positions on leg press. However, I only demonstrate six in my video. I find that I need to drop weight when my feet are closer together, so I do those at the end. Additionally, the lower the foot positions, the more stress is placed on the knees, so you may want to wrap them for stability.
Side note: I wear Asics 95% of the time due to under pronation, which are available at Fleet Feet.
Please note that I am not a personal trainer. This information is based on research and experience through exercise.