The words none, nun sound the same but have different meanings and spellings. Why do none, nun sound the same even though they are completely different words?
The answer is simple: none, nun are homophones of the English language.
No one; not one; nobody: None dared to do it.
Not any: None of my classmates survived the war.
No part; not any: none of your business.
Not at all: He is none too ill.
A woman who belongs to a religious order or congregation devoted to active service or meditation, living under vows of poverty, chastity, and obedience.
The 14th letter of the Hebrew alphabet. See Table at alphabet.
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").