This is a long story and situations have changed a number of times throughout the years.
Today the rules are whereever you are registered that is where you must use the pool or beach.
To give you an example, the beach at the Ocean Club is quite large and not nearly as packed as the Surf Club. People who own at the OC are happy about that (obviously) so if people from the Surf Club started going to that beach OC people would not be very happy. Same issue with the SC lazy river!