The words as, ass, asse sound the same but have different meanings and spellings. Why do as, ass, asse sound the same even though they are completely different words?
The answer is simple: as, ass, asse are homophones of the English language.
To the same extent or degree; equally: The child sang as sweetly as a nightingale.
For instance: large carnivores, as the bear or lion.
When taken into consideration in a specified relation or form: this definition as distinguished from the second one.
To the same degree or quantity that. Often used as a correlative after so or as: You are as sweet as sugar. The situation is not so bad as you suggest.
Any of several hoofed mammals of the genus Equus, resembling and closely related to the horses but having a smaller build and longer ears, and including the domesticated donkey.
A vain, self-important, silly, or aggressively stupid person.
The buttocks.
The anus.
Obsolete spelling of ass.
A small fox-like animal (Vulpes chama) of South Africa, valued for its fur.
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").