measure vs gauge

measure and gauge both are nouns.

Word	Noun	Adjective	Verb	Adverb
measure	Yes	No	Yes	No
gauge	Yes	No	Yes	No

As nouns, gauge is a hyponym of measure; that is, gauge is a word with a more specific, narrower meaning than measure:

measure: a basis for comparison; a reference point against which other things can be evaluated
gauge: accepted or approved instance or example of a quantity or quality against which others are judged or measured or compared

As verbs, gauge is a hyponym of measure; that is, gauge is a word with a more specific, narrower meaning than measure:

Other hyponyms of measure include scale, meter, pace, step, clock, time, fathom, sound, titrate, plumb, librate, weigh.

measure (noun)	gauge (noun)
how much there is or how many there are of something that you can quantify	a measuring instrument for measuring and indicating a quantity such as the thickness of wire or the amount of rain etc.
the act or process of assigning numbers to phenomena according to a rule	the distance between the rails of a railway or between the wheels of a train
any maneuver made as part of progress toward a goal	the thickness of wire
measuring instrument having a sequence of marks at regular intervals; used as a reference in making measurements	diameter of a tube or gun barrel
a container of some standard capacity that is used to obtain fixed amounts of a substance	accepted or approved instance or example of a quantity or quality against which others are judged or measured or compared
musical notation for a repeating pattern of musical beats
(prosody) the accent in a metrical foot of verse
a statute in draft before it becomes law
a basis for comparison; a reference point against which other things can be evaluated

measure (verb)	gauge (verb)
express as a number or measure or quantity	measure precisely and against a standard
determine the measurements of something or somebody, take measurements of	adapt to a specified measurement
evaluate or estimate the nature, quality, ability, extent, or significance of	mix in specific proportions
have certain dimensions	judge tentatively or form an estimate of (quantities or time)
	determine the capacity, volume, or contents of by measurement and calculation
	rub to a uniform size