hyperpyrexia vs pyrexia

hyperpyrexia and pyrexia both are nouns.

Word	Noun	Adjective	Verb	Adverb
hyperpyrexia	Yes	No	No	No
pyrexia	Yes	No	No	No

As nouns, pyrexia is a hypernym of hyperpyrexia; that is, pyrexia is a word with a broader meaning than hyperpyrexia:

hyperpyrexia: extremely high fever (especially in children)
pyrexia: a rise in the temperature of the body; frequently a symptom of infection

Other hypernyms of hyperpyrexia include hyperthermia, hyperthermy, febricity, febrility, fever, feverishness.

hyperpyrexia (noun)	pyrexia (noun)
extremely high fever (especially in children)	a rise in the temperature of the body; frequently a symptom of infection