This question might be far too broad, but I will ask it anyways.
My grandfather was theoretically ethnically Polish (at least, our name is Polish, and he spoke Polish). However, he always identified as "Prussian", as did his father and grandfather, who immigrated to the US around 1870. This confuses me.
Is there a Prussian ethnicity?
What were the distinct aspects of Prussian culture? Or was it just German culture?
Was Prussia ever distinct from Germany? Not just on a map, but in a cultural sense.
Why would an ethnic Pole identify as a Prussian? What was the relationship between the Poles living in Prussia and the state itself?
Long before the rise of Germany or Brandenberg, German settlers moved into the area of what was Danzig (I cannot remember the name of what it is now, but it's owned by the Russians now). This would become Eastern Prussia. The House of Hohenzollern came into possession of Prussia through marriage and allance with the Polish-Lithuanian Commonwealth in the 16th Century. From here, the House of Hohenzollern identified with Prussia after the HR Emperor allowed the House to be Kings in Prussia. From here, the political entity that is Prussia. Much of the lands considered Prussia are either in Russian or Polish hands right now.
Prussia wasn't really distinct from Germany, since Prussia actively pushed for German unification through politics and war. So it isnt correct to say Prussia was ever distinct from Prussia. However, I cannot speak about Prussia and German culture.