The words variance, variants sound the same but have different meanings and spellings. Why do variance, variants sound the same even though they are completely different words?
The answer is simple: variance, variants are homophones of the English language.
The act of varying.
The state or quality of being variant or variable; a variation.
A difference between what is expected and what actually occurs.
The state or fact of differing or of being in conflict. See Synonyms at discord.
Plural form of variant.
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.
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").