These are motte-and-bailey castles, many of which, though becoming private property of knights or aristocracy, began at the behest of the English king to help subjugate and control Norman-occupied England, and later Wales.
It is unlikely that much of a distinction was made between the two, but such castles were always useful for defence, as well as for providing a military presence in potentially rebellious areas, where perhaps the ambitions of the aristocracy meant they couldn't be entirely trusted.
During the turbulent history of medieval England, many aristocratic strongholds were seized in the name of The Crown, following changes in regime or internal disputes that left certain members of the aristocracy out of favour with the Monarch.
During the English Civil War, many Crown Fortresses fell prey to the Parliamentarian forces, and due to their strategic value were greatly fought for.
An even more historically recent fortress is Maunsell Sea Fort, built in the Thames Estuary during World War II.
Today many Crown Fortresses survive, even in state hands, although not necessarily as defensive structures—such as Fort George in the Scottish Highlands.