The words lay, lei, ley sound the same but have different meanings and spellings. Why do lay, lei, ley sound the same even though they are completely different words?
The answer is simple: lay, lei, ley are homophones of the English language.
To cause to lie down: lay a child in its crib.
To place in or bring to a particular position: lay the cloth over the painting.
To cause to be in a particular condition: The remark laid him open to criticism.
A garland of flowers, especially one worn around the neck.
Plural of leu.
Variant of lea.
Definitions 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").