How is the Hohenzollen dynasty related to the German monarchy?

Prior to the unification of Germany, the House of
Hohenzollern had held the Prussian throne for some time and had also been electors of
the Holy Roman Emperor. William of Hohenzollern was also William (spelled Wilhelm) first
of Prussia. His chief minister was Otto von Bismarck. Bismarck through a series of
machinations, managed to have Germany united under Prussian leadership. He did so by a
series of wars which appealed to German nationalism. Wilhelm I of Prussia became Kaiser
Wilhelm I of the German Empire when he was crowned at Versailles. Kaiser, of course, was
the German equivalent of "Caesar." He was succeeded later by his son Wilhelm II who was
the last Kaiser. He abdicated at the end of World War I and lived the rest of his days
in Switzerland.

There actually was no true German monarchy;
but there were two German Emperors, both of them Hohenzollern.