The words better, bettor sound the same but have different meanings and spellings. Why do better, bettor sound the same even though they are completely different words?
The answer is simple: better, bettor are homophones of the English language.
Greater in excellence or higher in quality.
More useful, suitable, or desirable: found a better way to go; a suit with a better fit than that one.
More highly skilled or adept: I am better at math than English.
Greater or larger: argued for the better part of an hour.
One that bets or places a bet.
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").