Mögen vs. wollen
The German words mögen, möchten, and wollen all translate to concepts of liking or wanting in English, but they are not interchangeable. They differ significantly in their level of politeness, the strength of the desire they express, and their specific context of use.
Mögen
A1The verb mögen primarily means to like. It expresses a general, ongoing preference or affection for a person, thing, or activity. It is not typically used to ask for something specific in the moment.
Ich mag meine neuen Kollegen.
(I like my new colleagues.)
Sie mag keine scharfe Soße.
(She doesn't like spicy sauce.)
Wir mögen es, im Park zu sitzen und zu lesen.
(We like to sit and read in the park.)
Magst du diesen Film?
(Do you like this movie?)
Das mag sein, aber ich bin nicht überzeugt.
(That may be, but I am not convinced.)
Wollen
A1The verb wollen means to want and expresses a strong, firm intention, will, or desire. It is very direct and can sound demanding or impolite if used for requests, especially with strangers. It is best used to state your own firm plans or when asking about someone else's definite intentions.
Ich will unbedingt diese Prüfung bestehen.
(I really want to pass this exam.)
Ein Kind könnte rufen: Ich will jetzt ein Eis!
(A child might shout: I want an ice cream now!)
Was willst du nach dem Studium machen?
(What do you want to do after your studies?)
Sie wollen nächstes Jahr ein Haus kaufen.
(They want to buy a house next year.)
Er will nicht zugeben, dass er einen Fehler gemacht hat.
(He doesn't want to admit that he made a mistake.)
Summary
In essence, use mögen for general likes ("I like chocolate"). Use möchten for polite, specific requests ("I would like a coffee"). Use wollen for strong intentions or firm plans ("I want to learn German"). For politeness, möchten is the safest and most courteous choice, while wollen is the most direct and can easily sound rude in the wrong context.