Summer garden and Summer Palace of Peter the Great

The Summer Palace, do you know where is it and which one of the Palace has this name oficially? People often use the name Summer Palace with different palaces which have absolutely different names. They often call the Great Palace in Peterhof - Summer Palace. The palace which actually has the name of the Summer palace is not so big and famous. But I consider it more important than the Great Palace. We know that the Great Palace in Peterhof was badly damaged by Nazis during the Second World War and a lot of things there were remaid. The Summer Palace in Summer Palace of Saint-Petersburg is small and cosy. But it survived all the wars and floods and there we can see original furniture and the floor - the things which Peter the Great and his wife Catherin were touching and using 3 hundreds years ago, can you imagine.