The words faux, foe sound the same but have different meanings and spellings. Why do faux, foe sound the same even though they are completely different words?
The answer is simple: faux, foe are homophones of the English language.
Artificial; fake: faux pearls.
A personal enemy.
An enemy in war.
An adversary; an opponent: a foe of tax reform. See Synonyms at enemy.
Something that opposes, injures, or impedes: taxes that were the foe of economic development.
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").