The words perse, purse sound the same but have different meanings and spellings. Why do perse, purse sound the same even though they are completely different words?
The answer is simple: perse, purse are homophones of the English language.
Dark grayish blue or purple.
A woman's bag for carrying keys, a wallet, and other personal items; a handbag.
A small bag or pouch for carrying money.
Something that resembles a bag or pouch.
Available wealth or resources; money.
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").