'Should do something' (no to) and 'ought to do something' have exactly the same meaning.

As Claire explained, the correct usage is "should do", but "ought TO do". Why does one modal verb use "to" while the other does not? I really don't know. I don't see any logical grammatical reason why it ought TO be one way or the other, but "should to do" sounds horribly wrong so you really ought not TO ever say it. (You really should not say it.)

They pretty much mean the same, but “ought to” is a lot more formal 😄

should is stronger