The words baited, bated sound the same but have different meanings and spellings. Why do baited, bated sound the same even though they are completely different words?
The answer is simple: baited, bated are homophones of the English language.
Simple past tense and past participle of bait.
Reduced; lowered; restrained; as, to speak with bated breath.
Simple past tense and past participle of bate.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License 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").