During the events of How to Betray a Dragon's Hero, Snotlout is later seen wearing and holding his Black Star, and it is used as a reminder to him of a time before he betrayed his family and tribe. Before he flies off on the Windwalker, Snotlout gives Hiccup his Black Star. In the epilogue Hiccup states that Snotlout and the Black Star are a part of his kingship. Hiccup also states that he wears Snotlout's Black Star with pride, as Snotlout was a hero in the end. Over the decades since he obtained the Black Star, Hiccup says that the black layer covering the Black Star faded away, and now it is only gold.
In How to Be a Pirate prior to the battle of the Lucky Thirteen, Stoick mentions the 'Black Helmet' award just before embarking on the quest to the Isle of the Skullions. This may be another distinct award, or it is possible the author meant it to be the 'Black Star' award. Nothing else is said about the 'Black Helmet'.
In which case you shall enter Valhalla a Hero of the Tribe! And may I say here, ... that anyone who dies in the course of his duty shall be awards a posthumous Black Helmet.