The words compleat, complete sound the same but have different meanings and spellings. Why do compleat, complete sound the same even though they are completely different words?
The answer is simple: compleat, complete are homophones of the English language.
Of or characterized by a highly developed or wide-ranging skill or proficiency: "The compleat speechwriter ... comes to anonymity from Harvard Law” ( Israel Shenker).
Being an outstanding example of a kind; quintessential: "Here was the compleat modern misfit: the very air appeared to poison him; his every step looked treacherous and hard won” ( Stephen Schiff).
Having all necessary or normal parts, components, or steps; entire: a complete meal.
Botany Having all principal parts, namely, the sepals, petals, stamens, and pistil or pistils. Used of a flower.
Having come to an end; concluded.
Absolute; total: "In Cairo I have seen buildings which were falling down as they were being put up, buildings whose incompletion was complete” ( William H. Gass).
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.