The words check, cheque sound the same but have different meanings and spellings. Why do check, cheque sound the same even though they are completely different words?
The answer is simple: check, cheque are homophones of the English language.
An action or influence that stops motion or expression; a restraint: Heavy rains were a check on the army's advance.
The condition of being stopped or held back; restraint: kept my temper in check; holding agricultural pests in check with sprays.
An abrupt stop in forward movement or progress; a halt.
The act or an instance of inspecting or testing, as for accuracy or quality; examination: the careful check of each unit before sale; gave the car an oil check.
Chiefly British Variant of check.
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.