The words lead, lede, lied sound the same but have different meanings and spellings. Why do lead, lede, lied sound the same even though they are completely different words?
The answer is simple: lead, lede, lied are homophones of the English language.
A leash.
To aim in front of (a moving target).
To show the way to by going in advance.
To guide or direct in a course: lead a horse by the halter. See Synonyms at guide.
A man; person.
Men; people, folk.
A people or nation.
Tenements; holdings; possessions.
A German art song for solo voice and piano.
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").