Grappling submissions are found in many different styles of the martial arts. You will find them in mixed martial arts, traditional arts, self-defense programs, and, of course, submission wrestling. On the surface, there may seem to be a great many different submissions which make up the totality of concession moves. This might be the perceptions but there really are not as many core submissions as you would think.
Generally, you have chokes and joint locks. Chokes are done through using apparel such as a Gi (Judo/Jiu Jitsu uniform) or naked when the arms or the legs are employed to deliver the choke. Joint locks entail a hyper-extension, a twisting motion, and, in some instances, a compression. These attacks can be performed on the upper or lower body joints.
Here is a look at the different grappling submissions which can be performed on the elbow. The well known straight armbar is a form of a hyper-extension. A kimura is an example of a twisting lock which can affect the elbow (and the shoulder) in a different manner. A bicep crusher would be among the most common form of a compression lock which causes pain on the elbow but the true damage which is being caused is the implosion of the elbow which can cause a major injury.
This does lead to another point about the concept of grappling submissions. Many who are not very familiar with how submission fighting works might assume there is no real chance of injury because they are watching the holds performed in a controlled manner with the intention of getting a concession from another athlete. These are not seen as a means of breaking a joint or trying to intentionally injure another person. What can be missed here is the obvious fact that someone quits a match when caught in a submission hold is due to the fact that something is about to be broken which is why someone quits.
Similarly, someone will quit a choke because of the fact they may be put to sleep. In some instances, a person caught in a choke will go to sleep trying to fight the choke to the bitter end. Very, very few fighters would be willing to have an arm or leg broken for no reason so they will begrudgingly tap out when caught in a joint lock. As the saying goes, you must live to fight another day. In this case, you will be able to fight another day because you have not suffered a severe injury as a result of a joint lock destroying your ligaments.
Grappling Submissions: The Bottom Line
In terms of the variety of different grappling submissions, the truth here is there are not all that many different submissions as much as there are scores of different entries to the submissions. So, you are not seeing all that many different finishing submissions but you are seeing quite a number of different setups and entries which can run into the thousands. You might never be able to document them all and you do not have to. All you need is to have a few high percentage ones in your toolbox.