Is Elmer's glue the same thing as PVA glue?
Yes, Elmer's glue is basically PVA.
Standard yellow wood glue (PVA glue) is the best TYPE of wood glue. Type 1 PVA - or waterproof PVA glue - should be used when any water exposure is possible, and on some woods is stronger than standard PVA wood glue. Most important is a tight fit and clamping. The brand of glue is not as important as the type.