alert vs alarm bell

alert and alarm bell both are nouns.

Word	Noun	Adjective	Verb	Adverb
alert	Yes	Yes	Yes	No
alarm bell	Yes	No	No	No

As nouns, alarm bell is a hyponym of alert; that is, alarm bell is a word with a more specific, narrower meaning than alert:

Other hyponyms of alert include torpedo, air alert, burglar alarm, fire alarm, foghorn, fogsignal, horn, red flag, siren, tocsin.

alert (noun)	alarm bell (noun)
a warning serves to make you more alert to danger	the sound of an alarm (usually a bell)
an automatic signal (usually a sound) warning of danger
condition of heightened watchfulness or preparation for action

alert (adjective)	alarm bell (adjective)
engaged in or accustomed to close observation
mentally perceptive and responsive
quick and energetic

alert (verb)	alarm bell (verb)
warn or arouse to a sense of danger or call to a state of preparedness