The words aught, ought sound the same but have different meanings and spellings. Why do aught, ought sound the same even though they are completely different words?
The answer is simple: aught, ought are homophones of the English language.
Anything whatever: "Neither of his parents had aught but praise for him” ( Louis Auchincloss).
Archaic In any respect; at all.
A cipher; zero.
Variant of aught1.
Variant of aught2.
Used to indicate obligation or duty: You ought to work harder than that.
Used to indicate advisability or prudence: You ought to wear a raincoat.
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.