Violence is any act which causes physical harm to another person. Hitting, slapping, punching, biting, scratching, whipping and many others are violent acts. Violence is indeed a part of BDSM. It falls under the S/m part, or sadomasochism, the giving and receiving of pain for pleasure. There are some differences between criminal violence and violence in BDSM. 

The largest difference between criminal violence and the acts which are done in BDSM is consent. In criminal violence, one does not have the informed consent of their victim. It is an act done usually on an unsuspecting person. In BDSM, the violent acts which are done are consented to by both participants. This consent overrides the moral issue of whether or not the act is criminal. By giving consent to the activities, it is understood that the people involved are aware of what is happening and accept it. Even, in many cases, crave it. Criminal violence is not wanted, craved nor even expected. BDSM violence is wanted, needed, craved and expected in many cases. 

Another difference is criminal violence is usually not controlled. It is done on the spur of the moment, with premeditated hostile intent, or any other number of non controlled means. Criminal violence does not take into consideration the permanent physical harm it causes, instead that is what it seeks to do cause permanent or temporary physical harm. In BDSM the violence is controlled. The strength behind the blows, the items used, the areas which are struck, the intensity of play and the length of time are all controlled by the dominant in the situation. This control is used in such a way to keep the experience pleasurable overall for both participants. This control is what prevents it from becoming an out of control act of violence. This control is what keeps the actions pleasurable and not torture. (be that pleasure physical or mental, or both) 

Another difference is the intent of the person being violent. A criminal's intent is usually one of causing the most damage they can, or furthering their own interests with any means necessary, subjugating their victim, or any other number of harmful reasons. A dominant's (or sadist's) intent for using violence is not to subjugate or harm the recipient. Instead it is to bring the recipient and him/herself pleasure. Through the violent acts inherent in pain play, the participants find a great physical and emotional satisfaction. The intent is to please each other, not harm each other.  

Another difference is the emotional state of the people involved at the time the violence occurred. In criminal violence, often the perpetrator is not emotionally stable, nor psychologically stable. Many times the violence comes about as a result of anger, fear or jealousy. All emotional states which can result in very irrational acts of violence. In BDSM, the emotional state of those involved usually contains some level of caring or love. The dominant and submissive are usually emotionally and psychologically stable. The violence comes about as a result of their bond and physical or mental needs. The violence becomes a way of sharing "love" with one another. A dominant or sadist, usually will not strike their partner when they are in the throes of anger, jealousy or fear. Many of the sessions are pre planned by the dominant, not just a grab em and beat em attitude.  

When many think of BDSM, all they see is the physical violence inherent in it. They dismiss it, ridicule it, or decry it as a criminal act. They say those who enjoy the s/m part  of BDSM do so because they are psychologically unstable or psychotic. Recently the psychological community changed it's definition of sadism, masochism, dominant and submissive to reflect the clearer understanding of the mentality behind those in the lifestyle. They are no longer defined as a psychosis or psychological illness. Instead, they are defined as mental and sexual acts which can be quite healthy provided they do not interfere with the normal functioning of the person involved on a daily basis. (meaning, the person can't function at their appropriate age level) If people take the time and look closer, they will see that the violence is just a means to an end in BDSM. The end result being a physical sensation that is more powerful than standard sex. An emotional bond that is all encompassing, and a psychological satisfaction that is quite healthy. They will see that many use the physical sensation of pain play to enhance their relationships, not destroy their partner.  

With the differences in intent, consent, and control clearly pointed out, one can see that BDSM violence is not a criminal act but one of enjoyment for those involved. As well, if one takes the time to truly discuss violence with those in BDSM they will see that most of us in the lifestyle abhor criminal senseless acts of violence. As well, we refuse to associate with those who are prone to such acts. Abuse in any form is looked down upon by those in the lifestyle.