That’s correct. A residency permit in any country in the Schengen zone allows you to travel freely within the respective countries, subject only to their individual immigration restrictions. ie you cannot spend more than 90 days in any individual country without registering and a residency permit in one country does not allow you to reside in any other country. So a PR card from Greece would allow you to travel to, for examle, 60 days in Italy, 70 days in France, 80 days in Spain etc but you could not move your residence to Spain.
As a practical matter, you could probably get away with spending longer than 90 days in a country as there are no checks, but the legal limit is 90 days.