fire alarm vs alarm system

fire alarm and alarm system both are nouns.

Word	Noun	Adjective	Verb	Adverb
fire alarm	Yes	No	No	No
alarm system	Yes	No	No	No

As nouns, alarm system is a hypernym of fire alarm; that is, alarm system is a word with a broader meaning than fire alarm:

fire alarm: an alarm that is tripped off by fire or smoke
alarm system: a device that signals the occurrence of some undesirable event

Other hypernyms of fire alarm include alarm, warning device.

fire alarm (noun)	alarm system (noun)
an alarm that is tripped off by fire or smoke	a device that signals the occurrence of some undesirable event
a shout or bell to warn that fire has broken out