The words mince, mints sound the same but have different meanings and spellings. Why do mince, mints sound the same even though they are completely different words?
The answer is simple: mince, mints are homophones of the English language.
To cut or chop into very small pieces.
To subdivide (land, for example) into minute parts.
To pronounce in an affected way, as with studied elegance and refinement.
To moderate or restrain (words) for the sake of politeness and decorum; euphemize: Don't mince words: say what you mean.
Plural form of mint.
Third-person singular simple present indicative form of mint.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.