Game of Thrones and House of the Dragon did not feature the same characters. This is not surprising, because the stories on which the projects were based unfolded in different time periods.
However, the families of noble houses appeared in both series. And this applies, first of all, to the Targaryens, whose representatives played the most important role in the plot of the films.
The central male character in Game of Thrones was embodied by Jon Snow, who for a long time thought that he was the bastard of the Starks. In fact, he was Aegon Targaryen, the illegitimate son of Rhaegar and Lyanna Stark.
This means that Kit Harington's character was blood related to the main character of House of the Dragon, Rhaenyra. If you trace the entire genealogy of the Targaryens, it turns out that there are many generations between these figures. Rhaenyra is Jon Snow's eighth-great-grandmother.
