Ownership is certainty of access and control. It must be distinguished between actual, moral, and legal.
Property is 'belongs to', whether properties of a word/thing or legal ownership. Property as a noun is the physically embodied capacity to be owned.
Rights are likewise properties, but in a less physically distinct sense; the right to expect certain behavior or forbearance from others belongs to the right-holder.
To say someone has property rights means that it is proper/right for them up have certainty of access and control.