In some parts of the world one needs only a single word for snow, but people in cold climates might distinguish between sleet, dendrites, needles and graupel. Similarly, the current world of limited liberty is accompanied by a limited vocabulary for liberty. With all the progress that libertarian theory has made in the last half century, it seems about time for language to start to catch up. There should not be just one vague notion of liberty, but many precise and nuanced concepts. Unfortunately, most people do not even have a good understanding of the words we already have.
Freedom is a word that is often considered synonymous with liberty, but liberty is actually a specific type of freedom. Freedom means without restriction or constraint. Liberty means being free from constraint imposed by other people. Liberty is freedom from conflict. It is freedom from having your life and goals interrupted by others. In a libertarian society, an individual has the freedom to do as he pleases, so long as he does not prevent others from doing as they please. Even if one achieves a state of liberty, they could still find more freedom by reducing the constraints of nature through technological progress. A person who is totally free can do whatever they want, uninhibited by the laws of nature, other people or even their own ignorance.1
The only freedom which deserves the name, is that of pursuing our own good in our own way, so long as we do not attempt to deprive others of theirs, or impede their efforts to obtain it. — John Stuart Mill, On Liberty 
Something that is closer to a synonym for liberty is the word crimeless. Liberty means a life without crime. No theft, murder, etc. The world may always have crime, but that does not mean we cannot strive for an ideal, crimeless society. We can work to reduce crime as much as possible. Which brings us to a word that is very important for the liberty minded: anarchy. The state is the most widespread denial of liberty and the greatest embodiment of crime. From the perspective of a single victim, the state may violate liberty less than say, a murderer. Yet, the state accounts for most of the murders in history, by an enormous margin. Anarchy may not be the final step for those interested in liberty, but it would increase liberty by such an enormous amount that the rest would seem like rounding error.
One cannot discuss the crimes of government without talking about war. One aspect of liberty is peace, because liberty requires the absence of war. Even if government cannot be abolished, its most vicious crime can be resisted. The state engages is many crimes on a massive scale, and one might argue that torture is more horrific, that taxation has more victims, or that more deaths come from regulations, but war is certainly the most overtly destructive crime perpetrated by government.
Anarchy is a word fraught with fear, uncertainty and doubt, so many people prefer the term individual sovereignty. Back in the day, there were kings. Kings could do whatever they wanted because they were sovereign. With liberty, everyone is king of their own life. They are sovereign, and it is good to be the king. People seem to like this word better than anarchy, but they are equivalent. A term similar to individual sovereignty is independence. If you are independent, you are free from external control. Total independence would include being independent from control by both the state and smaller criminal organizations. Another way to say this is autonomy. Liberty means being able to choose your own destiny, deciding what is best for your life.
So, when each person is free to choose their own path through life, it means that all human interaction is voluntary. When it is voluntary, all human interaction can be considered to be cooperation. Cooperation includes competition, like two soccer teams competing on a field or two companies competing on the market. If interaction is not voluntary, then there must be a victim and a crime has been committed. People should not be forced to participate in things that they do not agree with.
In an ideal world, no one would ever violate the non-aggression principle and liberty would be enjoyed by all. Unfortunately, even if the world were populated only with ardent libertarians, people would still accidentally cause property damage and make other mistakes. So liberty must be accompanied by the idea of justice. Justice means giving each man his due. This includes a life of liberty whenever possible, and then restitution whenever he is the victim of a crime. This is the only time when a person is due anything other than respect — namely, when his actions are interrupted and the life that should have been his is taken away. Whenever there is a crime, the life that could have been is gone forever. The best that can be done is to try to find ways to compensate for the loss.
In order to prevent this kind of situation, people develop right-of-way norms. Drive on a specific side of the road. The property system is just a practical application of libertarianism. It is a system of right-of-way norms called rights that specify how to behave so that people can coexist without conflict. It is a simplification of libertarian ethics that makes it easy to see whether a choice in behavior will lead to problems with others or not.
There are other concepts that are important to libertarianism, as well as new words that people have begun to try to coin. As libertarian theory continues to mature so will the idea of liberty and related concepts. Accordingly, the words used to express these concepts will evolve as well. This clarity of language will reinforce clarity of thought and help to bring about a more libertarian world.
1. If a man were totally free, he would not act. He would merely remake the world to suit him and enjoy it forever.