The words won't, wont sound the same but have different meanings and spellings. Why do won't, wont sound the same even though they are completely different words?
The answer is simple: won't, wont are homophones of the English language.
Contraction of will not.
Accustomed or used: "The poor man is wont to complain that this is a cold world” ( Henry David Thoreau).
Likely: chaotic as holidays are wont to be.
Customary practice; usage. See Synonyms at habit.
To make accustomed to.
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").