The words bowed, bode sound the same but have different meanings and spellings. Why do bowed, bode sound the same even though they are completely different words?
The answer is simple: bowed, bode are homophones of the English language.
To be an omen of: heavy seas that boded trouble for small craft.
Archaic To predict; foretell.
To be an omen; portend: The peace accord bodes well for the city under siege.
A past tense of bide.
Simple past tense and past participle of bow.
Having a bow, e.g. a bowed instrument is played with a bow
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, 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").