The words champagne, champaign sound the same but have different meanings and spellings. Why do champagne, champaign sound the same even though they are completely different words?
The answer is simple: champagne, champaign are homophones of the English language.
A sparkling white wine made from a blend of grapes, especially Chardonnay and pinot, produced in Champagne.
A similar sparkling wine made elsewhere.
A pale orange yellow to grayish yellow or yellowish gray.
A stretch of level and open country; a plain.
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").