What is morality?
Morality is the set of internal rules that members of a group should live by for the well-being of the society. Similarly, ethics is the set of external rules that members of a group should live by for the well-being of the group. So morality adjudicates your dealings with members of your own group just as ethics adjudicates your dealings with outsiders.
Morality is consequentialist. A rule is moral or immoral based on its theoretical consequences for the group that follows it. On the other hand, morality is non-consequentialist because it isn't too interested in the practical consequences of following a rule. If morality were wholly consequentialist, it would just be pragmatic.
What are rights?
Rights are the expectations one would have from a just society. These rights are organized hierarchically.
Human rights are universal, inalienable rights. They are universal because they apply to everyone equally. They are inalienable because they cannot be traded, negotiated, bought, paid for, sold, lost or destroyed. They can be violated or defended but they cannot be damaged, changed or taken away.
Human rights are positive. The terms "positive" and "negative" are purely a linguistic convention that has no meaning to non-Americans. It won't be explained here as it is ludicrous to limit humann rights by a linguistic convention. It should be noted that all so-called negative rights have a positive form but that not all positive rights have a negative form.
In particular, babies do have a positive right to be cared for and to be gazed at by their primary caregiver. When these rights aren't met, civilization collapses either directly by a population collapse or indirectly by a rise in psychopathy due to lack of bonding. The collapse of civilization isn't compatible with the well-being of society.
What are the human rights?
The Universal Declaration of Human Rights provides a good though imperfect listing of human rights. The most notable mistake is freedom of religion. Freedom of religion is not and can never be a human right because it directly contradicts freedom from religion which is a human right. Furthermore, freedom of religion cannot be established by a corrected Rawlsian process because atheists have no personal interest, no matter how minute, in protecting any freedom of religion. Finally it must be observed that if children have human rights, and they do, then they have the right to be free from their parents' religions. So in practice, within a few generations religion would die out.
What is Rawlsian morality?
Rawlsian morality is a process whereby you take a society of intelligent beings, scoop their brains out of their skulls to install them into vats, boost their intelligence, erase any particular knowledge of their history or circumstances (eg, personal life history, status, skin colour, nationality, language, proportions of same in the world), make them immortal, give them access to a database of all general knowledge (physics, cosmology, geology, biology, chemistry, psychology, economics, and so on) then let them deliberate between themselves what rules they are willing to live by.
This process works because it forces everyone to maximize their minimal expectations. There is no way for anyone to calculate the odds of their being killed if they're black versus if they're white. Likewise there is no way to calculate the odds of their getting away with raping someone. Or of their successfully killing their enemies. Everyone is forced to consider only one thing; their own skin. And short of people who are actively suicidal or masochistic, they all agree on much the same thing, right down to the ordering of human rights.