I feel "ought" is stronger and is something that is expected of you, but English is not my native language.

"You should drink more water"

"You ought to help your sick mother"

I'm a native speaker and I agree. "Ought" can connote an obligation or responsibility of some sort. "Should" is used more often when the outcome is out of any control. It might only be the speaker's belief.

But there is significant overlap.

That's when you turn to the RFC2119 all-caps requirement levels!