burglar alarm vs alarum

burglar alarm and alarum both are nouns.

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

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

Other hypernyms of burglar alarm include alarm, alert, warning signal.

burglar alarm (noun)	alarum (noun)
a warning device that is tripped off by the occurrence of a burglary	an automatic signal (usually a sound) warning of danger
a loud warning signal produced by a burglar alarm