The words styles, stiles sound the same but have different meanings and spellings. Why do styles, stiles sound the same even though they are completely different words?
The answer is simple: styles, stiles are homophones of the English language.
Plural form of <xref>stile</xref>.
Third-person singular simple present indicative form of <xref>style</xref>.
Plural form of <xref>style</xref>.
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.