billfish vs teleost fish

billfish and teleost fish both are nouns.

Word	Noun	Adjective	Verb	Adverb
billfish	Yes	No	No	No
teleost fish	Yes	No	No	No

As nouns, teleost fish is a hypernym of billfish; that is, teleost fish is a word with a broader meaning than billfish:

billfish: elongate European surface-dwelling predacious fishes with long toothed jaws; abundant in coastal waters
teleost fish: a bony fish of the subclass Teleostei

Other hypernyms of billfish include teleost, teleostan.

As nouns, teleost fish is a hypernym of billfish; that is, teleost fish is a word with a broader meaning than billfish:

Other hypernyms of billfish include teleost, teleostan.

billfish (noun)	teleost fish (noun)
giant warm-water game fish having a prolonged and rounded toothless upper jaw	a bony fish of the subclass Teleostei
elongate European surface-dwelling predacious fishes with long toothed jaws; abundant in coastal waters
primitive predaceous North American fish covered with hard scales and having long jaws with needlelike teeth
slender long-beaked fish of temperate Atlantic waters