I was comparing the USian president to the German chancellor. Both head up the government made up of ministers they appoint. It's only the name that is different, and the order in protocol. The USian president is first and head of state in protocol order, the German chancellor is third after the German federal president and the president of the Bundestag (one chamber of parliament).

Sorry for my being imprecise here, Germans tend to skip their own president(s) because, as you correctly state, they are mostly unimportant figureheads.