Modals. Less formal- more formal.

Hello teachers,
Am I right in these notes about these modals?
Should, had better, and ought to can express recommendation (advice) in present or future.
Should and had better are less formal than ought to. Ought to is more formal.
Can ‘recommendation’ and ‘advice’ be seen as synonyms in this case?

Thanks in advance.

This is my opinion:
1.Should > persuasive direction (or even a solicitation)
2.Had better > suggestive of advice (desirability of compliance)
3.Ought to > moral obligation (toward society, parents etc)
4.They have ‘present’ or ‘future’ connotations.
5.‘Had better’ is less formal (forceful) than others.
6.Can ‘recommendation’ and ‘advice’ be seen as synonyms in this case? > Not exactly.

(How a modal behaves often depends on the context, for a modal can indicate the mood of the speaker)

Anglophile,
Could you please explain your point of views with some examples?
Thanks.

Which of the above points of view?

Hello Anglophile,
Thank you your your reply.

RtL

Hello Anglophile,
Ought to (100% formal)
Should and had better are both less formal, but had better is even less formal than should; right?

RtL

I think it can be.