1,In the requests,"would like" is more polite than "want".
2,To give a wish,"want" sounds more confident than "would like" and when you use "want" for the wishes that surely they'll be done.
Examples:-I would like to pass the exam[just a wish,not sure i can or not]
-I want to pass the exam[i have prepared carefully & i can do it]
3,In the invitations,we use"would like",but "want" can't be used here.
Example:Would you like to go around the world with me?("Do you want to go...?"is just a question,not a invitation)
4,"wouldn't like" and "don't want" are different.
-"wouldn't want" can't be used in the invitations or request'cause it's not polite,so we use"don't want" or some else.
Example:Would you like some dishes?-No,i don't want any more,thanks./No,thank you so much/...
5,in the past form,"want" become"wanted",but "would like" is constant.
Example:Kumiko said,"I would like/want to help him"=>Kumiko said(that)she would like/wanted to help him.
6,"would like" has 2 other past forms to tell about one's wish which is just an illusion:
-"would like + to have Verb_past pasticiple"
or:"would have liked + noun/to verb/pronoun"
Example:I'd like to have lived on the Moon.
or: I'd have liked to live on the Moon.
HOPE IT WELL,Namfah^-^