Natural Right - a right that would exist in the absence of government
Right - a just claim or title
as humans we can have compassion and empathy with others, we can sympathize with their interests or position, we can put ourselves into their shoes and imagine our emotions and thoughts if we were them. we can champion the underdog in a conflict we are not involved in by imagining ourselves in the same position, and we can think of a bully or aggressor and say, "i would never act that way." this is perhaps the origin of our ability to claim moral judgments of the actions and conflicts of others, to say one is just and another is unjust.
but really, our ability to distinguish whats fair and unfair or right or wrong in a conflict is not really something permanent, inherent or inborn. how we perceive a conflict depends largely on the context of time and place. whether we sympathize with the stronger or weaker party in a conflict has a lot to do with our moral and religious training, and our own position in society and life.
for example, there are people who are so hypermoral that they consider eating meat wrong because it involves the 'unjust' killing of an animal. some are so hypermoral that if they see one animal kills another for food, they have an emotional reaction or sentimental response. they feel that the situation is unjust toward the weaker creature or perhaps empathize with it. so we see that learned moral sentiments can be extended ridiculously to nature where the rules that govern society would make no sense.
in the absence of law and government, or the rules of a society, if two persons or groups have a conflict over some property or over something else (people fight about all kinds of things, often without any of their actual interests being involved), there is no inherent or natural way to determine the justice of either party's actions. there is no inborn conception of justice that would allow all people to take the same side in the dispute. the number and kind of things humans would fight over in tribal times, from material things to non material, are probably innumerable.
lots of conflicts can have no just or unjust party, even if some sympathize with the one side, some with the other.
so then, the definition that a right is a "just" claim or title, and a natural right is "a just claim or title in the absence of government" can have no basis without a FINAL arbiter of the justice of the case.
not everyone agrees on the justice of any conflict. before governments, disputes were settled through feuds in which the parties' relatives took their cause as just because their feelings were toward their relative. that is as natural an impulse as any modern, trained moral impulse.
in the absence of the moral training that has come with centuries of civilization, religion and government, it is probably much more natural to side with whoever is closest to you than to try to niggle out the theoretical justice of the matter with "moral premises" that cannot be established or proven.
it is as likely in human nature to side with the stronger in a conflict then the weaker, neither is inherent or inborn. neither is provable as a theory.
justice has no natural or absolute properties. the conception of what is just comes from living in society and adhering to its rules and customs, and learning to seek one's interests in accord with those rules. as long as society provides protections and benefits, people will opt to be in rather than out, and will comply with its rules as the price for membership. crime is the refusal to pay that price, the attempt to free ride on society's protections without adhering to its rules.
society, law, rights -- they are social arrangements made to secure the interests of the members and make the conflicts that naturally arise in society resolvable through known laws and procedures, so that there is a predictable environment in which long term contracts and plans can be entered into. this allows economic activity, for one thing, because property is secure and contracts can be enforced.
we might strive for a society in which the conditions of the social arrangement are such that everyone is given absolute equal rights and allowed to pursue their private ends with the absolute least interference from others that is possible, consistent with the social structure continuing to exist. but whether this striving will have the support the the other members of the social arrangement will depend less on morality or justice than on their sense that their interests will be advanced by such an arrangement.
anyway - a right as "a just claim or title" has no meaning in the absence of a social arrangement in which custom and law bind the group to defend some individuals and punish others in order to limit and resolve conflicts and disputes.
in the absence of such an arrangement, all conflicts and disputes go to the bar of violence and power, and greater power is the only right or claim one can make and the only justice. it takes society to limit nature's form of justice and create man's justice.