Is there a difference in meaning between "must" and "should/ought to"?
e.g. You must not cross the road when the traffic lights are red[rule].
"Must" is most commonly used to express certainty. It can also be used to express necessity or strong recommendation, although native speakers prefer the more flexible form "have to." "Must not" can be used to prohibit actions, but this sounds very severe; speakers prefer to use softer modal verbs such as "should not" or "ought not" to dissuade rather than prohibit.
This must be the right address! [certainty]
Students must pass an entrance examination to study at this school. [necessity]
You must take some medicine for that cough. [strong recommendation]
Jenny, you must not play in the street! [prohibition]
source :ENGLISH PAGE - Must
Should = be supposed to
You should not cross the road when the traffic lights are red = You are not supposed to cross... You are expected not to cross...
He must see a doctor - He has to see a doctor [ he is not well/ he does not feel well]
He should see a doctor - He is supposed to see / expected to see.., because he is not well] -recommendation- gives a suggestion on what is the right thing for somebody to do
He ought to see a doctor - I recommend that he see a doctor.-indicates what somebody should do
Some other examples :
You ought to tell her how you feel. - You can't avoid telling her how you feel
You should tell her how you feel.- It is better or the best to tell her how you feel.
"Ought to" has the same intention as "should", that is to suggest something, but "ought to" says that you think that a person should pay more attention to your suggestion to give more importance to it.
"Ought to" is more specific than "should", more forcible.
Their meaning both point to the same direction, the basic difference is in the degree of expressiveness.
"ought to" is far closer to "there is nothing else/better to do but/except to" than "should"
(However there are several usages of "ought to" that are not the same as "should', I am talking here only about the part where they are similar in meaning.)
Here is a useful link: "Ought to" vs. "Should."