The words rude, rued sound the same but have different meanings and spellings. Why do rude, rued sound the same even though they are completely different words?
The answer is simple: rude, rued are homophones of the English language.
Relatively undeveloped; primitive: a rude and savage land; a rude agricultural implement.
Being in a crude, rough, unfinished condition: a rude thatched hut.
Exhibiting a marked lack of skill or precision in work: rude crafts.
In a natural, raw state: bales of rude cotton.
Simple past tense and past participle of rue.
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").