The words gage, gauge sound the same but have different meanings and spellings. Why do gage, gauge sound the same even though they are completely different words?
The answer is simple: gage, gauge are homophones of the English language.
Something deposited or given as security against an obligation; a pledge.
Something, such as a glove, that is offered or thrown down as a pledge or challenge to fight.
Archaic To pledge as security.
A standard or scale of measurement.
A standard dimension, quantity, or capacity.
An instrument for measuring or testing.
A means of estimating or evaluating; a test: a gauge of character. See Synonyms at standard.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.