Arrant and Errant have very close but different meanings. They began as different spellings of the same word, with the meanings of errant—(1) wandering and (2) wrong, as in sinful, mischievous, or disobedient—and these are still the meanings of errant; to err means “to make a mistake” and it also meant “to travel” long ago, but no longer.
Arrant began with these meanings, but now it means “extreme, in a bad way”; so, the cliché (from Shakespeare) “arrant knave” means “a completely untrustworthy person.” However, we don’t use knave much anymore, so you might say:
That guy is an arrant rogue.
Which would mean he’s completely uncontrollable. Arrant can also be used to describe things as well as people:
Your idea is arrant nonsense!
This means your idea is total nonsense.
Nowadays, some people may also use errant as if it means arrant; however, that is incorrect.