The words murr, murre, myrrh sound the same but have different meanings and spellings. Why do murr, murre, myrrh sound the same even though they are completely different words?
The answer is simple: murr, murre, myrrh are homophones of the English language.
A catarrh.
A purr (produced by any animal).
To purr.
Any of several large auks of the genus Uria, having black plumage and white markings.
An aromatic gum resin obtained from several trees and shrubs of the genus Commiphora of India, Arabia, and eastern Africa, used in perfume and incense. Also called balm of Gilead.
See sweet cicely.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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").