"Down the shore" versus "at the beach"
What is the difference between down the shore and at the beach? Does the latter imply you are physically on the beach?
Solution 1:
This is a New Jersey expression and refers to heading down south to any of the beach towns on the New Jersey shoreline.
Solution 2:
Consider that "the shore" in NJ was largely developed as resort communities for Philadelphia and New York during the summer months: in fact some resorts were built and owned by the railroads which took people there.
The beach is only part of the experience which included other attractions. In addition, many people have and had summer homes there.
"The Shore" is more a region than a location.