“Data rights” are a new set of rights that people should have but are not recognised by law (yet).
They are unlike:
copyright, because data rights apply to data whereas copyright applies to “works” (typically, works of art).
data protection, because data rights apply for the user uploading data, not for the person who is the subject of the personally identifiable data.
So data protection and data rights complement each others and some data is at the intersection of both of these rights.