https://en.wikipedia.org/wiki/Chordate A chordate is an animal of the phylum Chordata. Chordates are divided into three subphyla: Vertebrata (fish, amphibians, reptiles, birds, and mammals); Tunicata or Urochordata (sea squirts, salps); and Cephalochordata (which includes lancelets).
All fish are Vertebrates. All mammals are Vertebrates. Not all Vertebrates are fish. Not all Vertebrates are mammals. Fish are not mammals.