The words heald, healed, heeled sound the same but have different meanings and spellings. Why do heald, healed, heeled sound the same even though they are completely different words?
The answer is simple: heald, healed, heeled are homophones of the English language.
Alternative form of hield.
heddle
Alternative form of heald.
Simple past tense and past participle of heal.
Simple past tense and past participle of heel.
Having a heel (often specified, as in high-heeled etc.).
Prepared, especially armed with a weapon.
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").