The words whiled, wild sound the same but have different meanings and spellings. Why do whiled, wild sound the same even though they are completely different words?
The answer is simple: whiled, wild are homophones of the English language.
Simple past tense and past participle of while.
Occurring, growing, or living in a natural state; not domesticated, cultivated, or tamed: wild geese; edible wild plants.
Not inhabited or farmed: remote, wild country.
Uncivilized or barbarous; savage.
Lacking supervision or restraint: wild children living in the street.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, from The American Heritage® Dictionary of the English Language, 4th Edition 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").