Evidence: Audio.
My name is Amparo Mildre Guarín Morales. I belong to the course of comprehensive transport management technology.
I have a 17-year-old son, at this moment I live in Spain.

would like to
I would like to go visit him soon.
He would not like to get on a plane, He is terrified of it.
I asked him, 'Would you like to see the castles of Alicante?' and He answered that He would love to.

want to
He wants to study in Colombia.
He does not want to travel to Spain this year.
Could it be that... He does not want to see me?.

To + Infinitive to express a purpose
I work hard, to give my son a good education.
He will study diligently, to enter university.
I am going to work this year, to travel at Christmas.
I will save, to buy a house and thus be able to live peacefully.

Should
My son should make a psychology appointment; it would be appropriate to face his fear of getting on a plane.
I have not bought the tickets; I should buy them before they become expensive.
I should go to the doctor before traveling.
I should go on a diet, that way I would be thinner at Christmas.
I should not pack a lot of clothes in the suitcase; it would be very expensive for me.

MUST
My son must follow the traffic rules with his motorcycle.
I must carry my passport in order to travel without problems.
We must be prudent, so that our plans turn out well.
I am sad, because I must not travel with pets on the plane.

Semi-modal verb have to
I have to work from Monday to Friday.
I do not have to work on Saturdays or Sundays.
Do I have to work in December?
My son is graduating and He had to study every day.
He did not have to waste time at parties.
Did we have to work as a team to achieve it? Yes we did.

Muchas Gracias