Ballistic & Proprioceptive
Dynamic stretching is the lengthening of the muscles through gradual extension with motion. The muscle is tretched close to the end of range and then further stretched with a ballistic bouncing movement . This style of stretching should be conducted when the muscles are warm as it has a high risk of injury since you are stretching the muscle against resistance which causes a stretch reflex muscle contraction. This form of stretching is much more beneficial for particular sport or gym exercises where maximal range of motion is required such as squatting or ymnastics. It also prepares your nervous system for the demands of movement and prepares muscles and joints in a more specific movement manner.
Proprioceptive neuromuscular Proprioceptive neuromuscular is a stretching incorporates contraction and relaxation in an alternating form between the agonist and antagonist muscles. Agonist is the main muscle which moves the joint whereas the antagonist is the muscle which lengthens while the agonist is contracting. In elbow flexion the biceps are the agonist and the triceps are the anatogonist. There is the belief that greater muscle relaxation occurs after both agonist and antagonist contraction. Stretching normally requires a partner to help. Compared to static stretching it is though that stretching is superior for flexibility gains. However, like ballistic stretching there is the risk of over stretching.