Basic Technique Differences
Both exercises start with you lying on your back, legs bent and feet flat on the floor. With the sit-up you can either slide your feet under a stationary object or have a partner hold them down. Both exercises can be done with your fingertips placed just behind your ears or your hands crossed on your chest. For the sit-up, contract your abs, curl your torso completely off the floor as far as you can into a semi-seated position, lower back to the floor and repeat. You also contract your abs with the crunch, but you only lift your shoulders and chest off the floor -- your lower back remains on the floor.
While both exercises primarily target the rectus abdominis -- your abs -- the sit-up also engages your hip flexors, the iliopsoas and several assisting muscles, the obliques, rectus femoris, and tensor fasciate latae. The additional muscles are worked during the sit-up because once your shoulders and chest are off the floor, your hips must bend in order to raise your torso as far as you can. The risk of back injury is greater with sit-ups because of the involvement of the hip flexor muscles. With the crunch, you only bend your waist slightly to raise just your shoulders and chest. This action doesn't involve your hips as the obliques are simply assisting muscles.