Bremen was a city in the Hanseatic League founded in the 13th century. It is 60km south of the mouth of the Weser where the river enters the North Sea. Bremerhaven is at the mouth of the river, i.e. 60km from Bremen, a quite separate city founded in 1827 as ships began to be too big to navigate the higher reaches of the Weser to get to the Port of Bremen, but this did not mean that Bremen ceased to be a port. Two completely different cities. However the city of Bremerhaven which did not even exist at the time of the Hanseatic League, is included in the modern "Land" (state) of the Freie Hansestadt Bremen (Free Hanseatic City of Bremen) which is a "Land" (state) in the modern Federal Republic of Germany. Your ancestor left from either Bremen or Bremerhaven so looking for records will require knowing which port it was.