The words moo, moue sound the same but have different meanings and spellings. Why do moo, moue sound the same even though they are completely different words?
The answer is simple: moo, moue are homophones of the English language.
To emit the deep, bellowing sound made by a cow; low.
The lowing of a cow or a similar sound.
A small grimace; a pout.
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.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").