The words taught, taut sound the same but have different meanings and spellings. Why do taught, taut sound the same even though they are completely different words?
The answer is simple: taught, taut are homophones of the English language.
Past tense and past participle of teach.
Pulled or drawn tight; not slack. See Synonyms at tight.
Strained; tense: nerves taut with anxiety.
Kept in trim shape; neat and tidy.
Marked by the efficient, sparing, or concise use of something, such as language or detail: a taut movie script.
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.