rain gauge vs rain gage

rain gauge and rain gage both are nouns.

Word	Noun	Adjective	Verb	Adverb
rain gauge	Yes	No	No	No
rain gage	Yes	No	No	No

As nouns, rain gauge and rain gage are synonyms defined as:

rain gauge and rain gage: gauge consisting of an instrument to measure the quantity of precipitation

Other synonyms of rain gauge include pluviometer, udometer.

rain gauge (noun)	rain gage (noun)
gauge consisting of an instrument to measure the quantity of precipitation	gauge consisting of an instrument to measure the quantity of precipitation