Earlier quoted context omitted.
Libertarianism is basically about negative rights - not so much about "do what you want", but more about "nobody is going to force you to do something you don't want". As an ethical system, think of it as utilitarianism which assigns infinite value to freedom from violent coercion. Everything else follows from that.
Unless it's violent coercion used to enforce the property system, which libertarians seem to like to ignore.
But yes, that is the next most important division. Right libertarians believe that there is a natural right to property ownership. Therefore, infringement on that right is an aggression, and using violence to protect it is simple self-defense. Left libertarians believe that private property is a social construct, and that it has negative social effects at large scale (a few would even say that it has them at any scale), and so reject it, and the use of violence to protect it.