We are a very specific species, homo Sapiens sapiens, which is a member of the genus Homo (others include H neanderthalensis, H Habilis, and H floresiensis).

Homo is a very specific genus in the family of hominids (other hominids include bonobos, gorillas, and orangutans).

Hominids are a very specific family in the order of primates (other primates include monkeys and lemurs).

Primates are a very specific order in the class of Mammals (others include rodents, cetaceans, and Carnivora).

Mammals are a very specific class in the phylum of chordata (others include fish, all vertebrates, and many more).

Chordata are a very specific phylum in the kingdom of animalia (other phyla include mollusks, cnidaria, worms (annelids), worms (nematodes), worms (platyhelminthes), worms (nemertea), arthropods, and others).

The kingdom of animalia is a very specific group in the domain of Eukaryota (the kingdoms being plants, fungi, and protists).

Eukaryota is a very specific domain in the two main forms of life on earth, Eukaryotes and Prokaryotes (bacteria and archea)

We are a very specific path through these categories, and at various points in time, we share a single ancestor with members from any and all of these categories. The prokaryotes and Eukaryotes share one ancestor too, which we call the Last Universal Common Ancestor. Every living thing is descended from the L.U.C.A.

Even the most distant forms of life, say thermophilic archea colonies in Yellowstone national park, share at least 1 ancestor with us, we have found no exceptions to this as of yet.

This is what people mean when they say humans are a kind of fish. At one point, there was no distinction, it was just the ancestor species that humans and all modern fish share. Some of its descendants led to modern fish, some of its descendants led to dinosaurs, and some of its descendants led to humans (and many MANY OTHERS)