The words storey, story sound the same but have different meanings and spellings. Why do storey, story sound the same even though they are completely different words?
The answer is simple: storey, story are homophones of the English language.
Chiefly British Variant of story2.
An account or recital of an event or a series of events, either true or fictitious, as:
An account or report regarding the facts of an event or group of events: The witness changed her story under questioning.
An anecdote: came back from the trip with some good stories.
A lie: told us a story about the dog eating the cookies.
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").