Some contrasts of the two are as follows. Human rights give me the right to be free of tyranny and abuse by government, society, or individual. Cultural rights give me the right to send my child to school without fear for their physical safety or social and moral corruption. Human rights give me the right to food, medical care, and education. Cultural rights give me the right to free, unrestricted access to my culture's advantages. There is some seeming overlap between categories of rights though the difference is between individual versus collective application of the rights.
What is interesting about this whole question is the way in which human rights and cultural rights can sometimes be seen to overlap. Interestingly, the example of language was given above. This is and always has been a very interesting issue for some minority groups who might be slowly dwindling in number because of the way that they are incorporated (or not) into the society of which they are a part. Is the right to speak their language part of their identity as humans or is it just a cultural right?
People have certain basic human rights which are required in order to thrive as a living being. Nourishment, shelter, safety from physical and emotional harm, recognition and support from others, finding a purpose for existence - these kinds of things are human rights. They all need to be met for a person to live a healthy life.
Cultural rights are dictated by the cultural norms of a given area and may vary greatly from place to place. Previous posts have given good explanations of some of the factors that may influence what are accepted as the cultural rights implicit in a given locale. The differences in cultures, and the resulting differences in rights and expectations, are some of the reasons why moving from one culture to another can be so challenging. If the cultural rights of the new area are very different from those of the previous location, the result can be significant culture shock!
One way in which human and cultural rights conflict is in the custom of circumcision. This coming of age rite is particularly troubling in the case of female circumcision, which seems to be a clear violation of human rights, but an authentic cultural custom. Should it be made illegal, even though it is a cultural custom? Few people outside the cultures which practice it can find a good argument in its defense, and I would imagine that even many within the culture oppose it. Even in the case of male circumcision, shortly after birth, which is a requirement in Judaism, there are those that find this to be a violation of human rights. I believe an ordinance was proposed in San Francisco, making this an illegal act within the city limits. I don't know if it passed, but if it did, it will make for a very interesting test of the First Amendment, which is supposed to sort out this sort of tension for us.
Human rights are those things that every human being, in every society and country, have a right to. The UN Declaration of Human Rights in 1948 spelled out more than 30 of these the world agreed to, including freedom from torture, from human trafficking and slavery, and freedom to have your own identity and nationality.
Cultural rights are more vague, and in my mind, less protected. Saudi Arabia discriminates against women in many ways, but some would argue that is their culture and has been for generations, so they have a right to practice it without world interference. In this way, cultural rights and human rights are sometimes at odds with each other.
Human rights are the right to live and be relatively free to live your own life without interference. Cultural rights are the rights to believe as you wish, and practice your own customs. The difference is that while culture is uniquely human, not all cultures are the same. Some people's cultural beliefs are offensive or frightening to others.
Human rights are the rights that all people have simply by the fact that they are human. These are things like the right to freedom of speech or the right to life that do not depend on what group a person belongs to.
Cultural rights, by contrast, are the rights that various cultures have to survive. For example, the right that a culture has to preserve its language is a cultural right. These rights are similar to human rights in that all cultures have them (say rights advocates). However, they are different because they are not rights that reside in the individual. Instead, they are rights that are held by a society as a whole.