The words adieu, ado sound the same but have different meanings and spellings. Why do adieu, ado sound the same even though they are completely different words?
The answer is simple: adieu, ado are homophones of the English language.
Used to express farewell.
Bustle; fuss; trouble; bother.
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.