The words wailed, whaled sound the same but have different meanings and spellings. Why do wailed, whaled sound the same even though they are completely different words?
The answer is simple: wailed, whaled are homophones of the English language.
To grieve or protest loudly and bitterly; lament. See Synonyms at cry.
To make a prolonged, high-pitched sound suggestive of a cry: The wind wailed through the trees.
Archaic To lament over; bewail.
A long, loud, high-pitched cry, as of grief or pain.
Plural form of whale.
Third-person singular simple present indicative form of whale.
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").