I think I can.Oh Chris...no. I don't think you can re-define it that way
Where I live, the self defense is described as a use of an amount of physical force against other person necessary and sufficient to avert, avoid or prevent an assault on yourself or another person.
Violence on the other hand is described as a use of physical force to injure, abuse, damage, or destroy.
So there is a line between the self defense and violence defined by the amount of force and the intent and they ARE defined as two separate things. Naturally there is a grey area between them and you can easily turn your self defense into an assault by using unreasonable amount of force (Which in our law system is loosely defined as using an attack that causes more harm than it potentially prevents (i.e. don't bring a gun into a knife fight))
So on purely personal level, you actually CAN distinguish between the two.