Each of the expressions möchte, will, lieber, würde seems to mean I want / I wish / I’d like.
Was würden Sie gern essen?
Can you help me to understand the difference between them?
I think this is very well explained here. I hope this helps.
Willst du is 2nd person singular of wollen. It is a desire coming from your will/head rather then a hearts wish. When you order in a restaurant you often choose möchten (subjunctive of mögen) than wollen, because it is much more polite.
Ich will ... = I want ...
Ich möchte ... = I'd like ...
Also refer to this Q&A: "Ich möchte das gerne machen" or "Ich würde das gerne machen"