They like the 'Prussia' that the Hohenzollerns ruled, which came to go by "Prussian" mainly because it was their territory outside the HRE so they could call themselves kings in it/of it.

For some reason they never talk about the pagan Old Prussia that was invaded by the Teutonic Knights and subjected to Germanization (i.e. cultural genocide) by from the Northern Crusade until their language and culture ceased to exist.