The words wrights, writes, rights, rites sound the same but have different meanings and spellings. Why do wrights, writes, rights, rites sound the same even though they are completely different words?
The answer is simple: wrights, writes, rights, rites are homophones of the English language.
Plural form of right.
Third-person singular simple present indicative form of right.
Plural form of rite.
Plural form of wright.
Third-person singular simple present indicative form of write.
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").