hellfire vs Inferno

hellfire and Inferno both are nouns.

Word	Noun	Adjective	Verb	Adverb
hellfire	Yes	No	No	No
Inferno	Yes	No	No	No

As nouns, Inferno is a hypernym of hellfire; that is, Inferno is a word with a broader meaning than hellfire:

hellfire: a place of eternal fire envisaged as punishment for the damned
Inferno: (Christianity) the abode of Satan and the forces of evil; where sinners suffer eternal punishment

Other hypernyms of hellfire include Hell, infernal region, nether region, perdition, pit.

hellfire (noun)	Inferno (noun)
a place of eternal fire envisaged as punishment for the damned	(Christianity) the abode of Satan and the forces of evil; where sinners suffer eternal punishment