burglar alarm vs alarm system

burglar alarm and alarm system both are nouns.

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

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

burglar alarm: a warning device that is tripped off by the occurrence of a burglary
alarm system: a device that signals the occurrence of some undesirable event

Other hypernyms of burglar alarm include alarm, warning device.

burglar alarm (noun)	alarm system (noun)
a warning device that is tripped off by the occurrence of a burglary	a device that signals the occurrence of some undesirable event
a loud warning signal produced by a burglar alarm