The words rained, reigned, reined sound the same but have different meanings and spellings. Why do rained, reigned, reined sound the same even though they are completely different words?
The answer is simple: rained, reigned, reined are homophones of the English language.
Simple past tense and past participle of rain.
Simple past tense and past participle of reign.
Simple past tense and past participle of rein.
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").