These two words sound alike, but taught and taut have different meanings. Taut is an adjective meaning tense or tight. Taught is the past (and past participle) form of the verb teach.

taut

(adjective): “The ad promised that the face cream would make my skin smooth and taut.”
Her nerves were taut as she awaited the results.

taught

(verb): “She taught me everything I know about photography.”
“I have been taught by renowned experts in the field.”

Remember:

Taut is similar to tight (“Pull the rope taut.”)

The past tense of teach is NOT “teached.”

“He teached me how to play stickball.” X

“He taught me how to play stickball.” ✓