The words calyx, calix sound the same but have different meanings and spellings. Why do calyx, calix sound the same even though they are completely different words?
The answer is simple: calyx, calix are homophones of the English language.
Ecclesiastical A chalice.
The sepals of a flower considered as a group.
A cuplike structure or organ, such as one of the cuplike divisions of the pelvis or of the kidney.
A collecting structure in the kidney.
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").