Although many references state that Operation Neptune refers to the naval operations in support of Operation Overlord, the most reliable references make it clear that Overlord refers to the establishment of a large-scale lodgement in Normandy, and that Neptune refers to the landing phase which created the beachhead; i.e. Neptune was the first part of Overlord. According to the D-day museum:
The armed forces use codenames to refer to the planning and execution of specific military operations. Operation Overlord was the codename for the Allied invasion of north-west Europe. The assault phase of Operation Overlord was known as Operation Neptune. (...) Operation Neptune began on D-Day (6 June 1944) and ended on 30 June 1944. By this time, the Allies had established a firm foothold in Normandy. Operation Overlord also began on D-Day, and continued until Allied forces crossed the River Seine on 19 August 1944.