"Aught" is archaic for "anything at all." Since it's archaic, it just isn't used anymore in modern English in nearly all practical situations. Use it only for 'special effect,' if you get my general meaning.
So you're left with "ought," which basically means "must" in most practical cases. Back in my schooldays over 40 years ago, the memory aid is that "ought" and "order" (must) both start with letter O.
We ought to respect the law. (The law 'orders' us to respect it.) - Quora
Another good one I could think of is
'Ought' has same letters as 'Tough'
Meaning that it indicates compulsion and force.
I always suggest ignoring the second word when you have only two words to differentiate. That way you are saving memory and makes it easy to remember the one and only fact. When time comes you'll magically know to use the 2nd word if the first one is not applicable.