The words gray, grey sound the same but have different meanings and spellings. Why do gray, grey sound the same even though they are completely different words?
The answer is simple: gray, grey are homophones of the English language.
Of or relating to an achromatic color of any lightness between the extremes of black and white.
Dull or dark: a gray, rainy afternoon.
Lacking in cheer; gloomy: a gray mood.
Having gray hair; hoary.
Variant of gray1.
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").