Static stretching
Static stretching can be divided to active and passive. In active stretching the position is kept over 30 second, there are no movement only your own pressure. Passive stretching is the same as active, but the pressure is created with some tools or partner, when your own body remain relax.
Static stretching might affect negatively to explosive performance if they performed before the performance. Static stretching increase range of motion so it would be good to do them after performance or day before.

Dynamic stretching
Dynamic stretching include movement, which gradually reach the limits of the movement. These are often sports specific stretching and can help improve movements that are required. For example, for runner this might be stride length.
Dynamic stretching are good during the warm up, as they also increase blood flow.

Ballistic stretching
Ballistic stretching are rapid bouncing movements which go beyond of the range of motion. These forces the muscle stretch for the short period of time and then relax. These bouncing movement are performed several times. Ballistic stretching are good to increase the range of motion, but the injury risk is high. It would be good to perform them after static stretching and when body is warmed up.

Active isolated stretching (AIS)
AIS are performed in reps, body are reached some position hold it in there couple second without any assistance or equipment, then released and performed again 10 times. High kick are good example. They increase blood flow and fascia elasticity.

Proprioceptive Neuromuscular Facilitation (PNF)
PNF involves several types of stretching types and often performed with partner. For example first isometric hold which after static stretching. It’s one of the best technique to improve range of the motion.
Muscle energy technique (MET)
There are several opinions about PNF and MET, are they a same or not. Some think they are the same, but others disagree, says that MET use person’s ability to use inherent energy to relax muscles whereas PNF use person’s understanding of the movement and thus ability to relax muscles. Techniques are the same as MET also require partner, which stretches the client in the static position a while, after that client push towards a few seconds and relax again, when partner can push stretching position slowly deeper.

Isometric Stretching
Isometric stretching are simple version of PNF. Isometric stretching also require partner, which stretches muscles in the one position and client resisting it. During PNF, there are passive static stretching-isometric stretching-deeper passive static and so on.
Isometric stretching are good when there are needs to increase the range of motion, but body need to be warmed up before performing these, also they are not the best option before the performance.