The Amsterdam ship Star or Morgenstar

We had seen a ship named Morgenstar mentioned as being in the Mediterranean Sea prior to the First Anglo-Dutch War. This seems to be the same ship called Star in 1652 and early 1653 and which was commanded by Jacob Pauwelsz Cort. This same ship, also called Morgenstar was commanded from May 1653 by Albert Claesz Graeff. He commanded the Morgenstar in the Battle of Scheveningen. One possibility is that they were different ships, but we think that they were the same ship. For one thing, you don't see the two ships in service with the fleet concurrently. Jacob Pauwelsz Cort eventually became Michiel De Ruyter's flag captain in the new ship Huis te Cruiningen, which had been purchased from Genoa while under construction.