【Standard】 ,  【criterion】 ,  【gauge】 ,  【yardstick】 ,  【touchstone】  can all mean a measure by which one judges a thing as authentic, good, or adequate or the degree to which it is authentic, good, or adequate.

【Standard】 applies to an authoritative rule, principle, or measure used to determine the quantity, weight, or extent or especially the value, quality, level, or degree of a thing.

【Criterion】 denotes the thing, whether formulated into a rule or principle or not, by appeal to which one arrives at or confirms a given judgment (as of value, quality, fitness, or correctness).

【Gauge】 , concretely a 【standard】 measure or scale or an instrument for measuring something that fluctuates (as in size or height), can in extension apply to a 【standard】 measure whether tangible or not.

【Yardstick】 , basically a measuring stick a yard long and subdivided into inches and fractions of inches, is often extended to standards or criteria especially for something intangible or immaterial.

【Touchstone】 can apply to a simple device by which authenticity or value may be determined and especially to an authentic or superior instance of a class of things by comparison with which another thing may be judged authentic or superior.