What?
Storm's End is a Castle, the seat of House Baratheon who rule the Stormlands.
Dragonstone used to be the seat of the heir to the throne located on the Blackwater. One of the reasons Stannis was always upset with Robert was because he took Storm's End from him, the family seat, and gave him Dragonstone while giving Renly Storm's End instead. Robert said this was to "honor" him since he was the heir at the time as he hadn't had any children with Cercei, but he never corrected the situation after Cercei gave "him" children.
My bad. I got the name Storm's End confused with the Stormlands.