From a comment here, in frequent usage, arse and ass are often interchangeable when used to refer to buttocks or to a person of dubious charms. However, although “to arse about” has a vague connection to “make an ass of oneself”, many of the threads of meaning derived from arse are not present in ass. Likewise, ass has a donkey-referring component that arse does not.
Despite common perception, are these words more deviant than common usage indicates?
Edit: It appears they have (someone look this up with an authoritative dictionary please) different origins, asinus (Latin) for ass, and ærs (Old English) or orros (Greek) for arse.