want |wänt, wônt|
verb
1 [ with obj. ] have a desire to possess or do (something); wish for: I want an apple
like 2 |līk|
verb [ with obj. ]
2 wish for; want: would you like a cup of coffee? | I'd like to rent a car | [ with obj. and infinitive ] : I'd like you to stay | [ no obj. ] : we would like for you to work for us.
The meanings are quite close. "would like" in some circumstances is more polite. If you are at the dinner table and someone offers you something, "Yes, I would like some" is perhaps slightly more polite than "Yes, I want some".