Like how all squares are rectangles, but not all rectangles are squares; What we ought to do is always what we should do, but what we should do is not always what we ought.
Ought has the notion of being "morally based" in its common use as well standard definition. What we think we "should" do can arise from fear, habit, morals and a number of other things. That's not to say sometimes these same things can't help come to a moral conclusion.