Most text books will tell you there are two types of stretching, just passive and active but I am going to give you four types.
Active stretching is using dynamic movements to allow the body to warm-up and open up. The sun salutations in yoga could be a form of active stretching. Generally you should do active stretching to prepare the body for activities such as running, sports, or working out using movements that mimic the activity.
Passive stretching is holding a stretch for a set period of time. Most books I have read tell you that you can hold a stretch from 10-60 seconds. I have found it takes most people at least a full minute for the body to actually relax into a stretch and make progress. It is my belief that if you are holding a stretch and don't feel a release then you are only maintaining your current level of flexibility. You need to feel the release and then stretch a little further as your body allows to actually improve your flexibility.
Research is showing to do active stretching before you exercise and passive stretching after. Passive stretching has been shown to decrease power and explosiveness. However, it is important to listen to your body and find what works best for you and your situation. I listened to a podcast with Mike Boyle, a strength and conditioning specialist, and he found his athletes performed better and had less injuries when using passive stretching before a workout.
PNF and resistance stretching is similar to passive stretching as you are holding a stretch. The difference is that for a period of time you will be contracting the muscle and then relaxing back into the stretch. This produces a response in the Golgi Tendon Organ that allows your body to relax deeper into the stretch. There are some stretches you can do on your own using this method but there are a lot more you can do with a partner. I have seen amazing results using this method with clients whose main focus is to increase their flexibility. When I teach PNF courses and the students start practicing on each other the room is always full of "wow" and other shock and surprise on how effective it is in such a short time.
Thai Yoga Massage is another category of it's own. I have never seen this discussed as its own type of stretching but after much practice I believe it is. This is an entire system of passive stretching that is combined with joint rotation, traction, and massage that helps the body increase flexibility and improves chronic issues. I have seen extreme results in flexibility and posture using Thai Yoga Massage. The closer the sessions are together, the more flexibility results I see.
Active and passive stretching are the two types you can do on your own. PNF, resistance stretching, and Thai Yoga Massage require a trained professional. Perhaps that is why most text books say there are only two types of stretching!
If you want to learn more about stretching, I have an online program called Simply Stretch that will give you four simple routines that will last a lifetime and it's only $35. It's available in the Online Wellness Studio.