Prussia was a powerful north German state around which the other German states unified after the Franco-Prussian War in 1870-71. It was ruled by the Hohenzollern Dynasty, whose kings became known as "the German Emperors" after the unification of Germany. Prussia maintained a substantial level of autonomy within the empire. After World War I, Prussia became a Free State of the Weimar Republic. With the rise of the Nazi Party, Prussian autonomy was curtailed. After World War II, the Western Allies abolished Prussia, redividing it into several other states.
In the midst of the Thirty Years' War, Prussia was the Duchy of Prussia, centered around Königsberg (modern-day Kaliningrad). While nominally a Polish fief, it was governed by the Hohenzollern Dynasty, in a personal union with Brandenburg that was sometimes referred to as Brandenburg-Prussia. The Duchy of Prussia was east of Brandenburg, and separated from it by Polish territory.
Due to the early unification of Germany by the up-timers and their Swedish Allies, Brandenburg-Prussia just becomes another territory of Germany. It's historical importance gone in this Alternate Universe.