The words hae, hay, hey sound the same but have different meanings and spellings. Why do hae, hay, hey sound the same even though they are completely different words?
The answer is simple: hae, hay, hey are homophones of the English language.
Scots To have.
Grass or other plants, such as clover or alfalfa, cut and dried for fodder.
Slang A trifling amount of money: gets $100 an hour, which isn't hay.
To mow and cure grass and herbage for hay.
To make (grass) into hay.
Used to attract attention or to express surprise, appreciation, wonder, or pleasure.
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").