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You have made some good distinctions. Let me add one more.

Political philosophers commonly distinguish between non-interference rights and welfare rights.

Non-interference rights are rights not to be restrained or not to be prevented from doing what we want to do by institutions or other people. For example, if I have a non-interference right to go to California, no one has the right to physically prevent me from doing so. In some cases, a non-interference right specifies that a specific party cannot interfere with my doing a certain thing. For example, the first amendment indicates that "Congress" shall make no law "abridging the freedom of speech." It is specifically congress that is restricted by this right. (One of the best schemas for thinking about rights is that a right is a freedom from X to do Y. In my example, X is congress. It might be something else.)

Notice that my non-interference right to go to California does not guarantee me the money I need to go to California. Likewise, my non-interference right to publish a book does not guarantee me a publisher or a printing press. My right to speak does not guarantee me a forum at Carnegie Hall. All those rights to various resources go beyond a right to non-interference.

Welfare rights are usually thought of as rights to specific goods and services such as food, medical care, or housing. A welfare right could be thought of as a natural right or a statutory right. We can prove that a person has a statutory right to housing by pointing to certain provisions in the law. To establish a natural right to housing would require a completely different approach. In some cases, people argue that everyone should have a statutory right to Z because they have a natural right to Z.

In the United States, we have a fairly strong tradition of recognizing certain statutory non-interference rights, but welfare rights are a more recent phenomenon and remain controversial. Does everyone have a natural right to basic medical care? Should everyone have a statutory right to basic medical care? We are still arguing about this sort of issue.