der Wunsch
wish
An inner desire or the hope that something specific will happen or that you will get something.
Ihr größter Wunsch war es, einmal im Leben das Meer zu sehen.
Her greatest wish was to see the sea once in her life.

wish
Loading your saved state.
wish
An inner desire or the hope that something specific will happen or that you will get something.
Ihr größter Wunsch war es, einmal im Leben das Meer zu sehen.
Her greatest wish was to see the sea once in her life.

The noun 'der Wunsch' (wish) is closely related to the verb 'wünschen' (to wish). When you wish for something, you have a Wunsch (wish).
Ich wünsche mir ein neues Fahrrad.
I want a new bicycle.
'Wunsch' (wish/request) is often combined with certain verbs. You can 'haben' (have) a wish, 'äußern' (express) it, and someone can 'erfüllen' (fulfill) a wish.
Er hat den Wunsch geäußert, befördert zu werden.
He expressed the wish to be promoted.
An inner wish is often described more precisely with an infinitive construction with 'zu' (to) or a 'dass' (that) clause. Both follow directly after the noun.
Sein Wunsch, Pilot zu werden, war sehr stark.
His wish to become a pilot was very strong.
To express a general, often abstract desire, you use the preposition 'nach' followed by the dative.
Nach dem langen Winter ist der Wunsch nach Sonne groß.
After the long winter, the desire for sunshine is strong.
The expression 'auf Wunsch' (upon request) means that something is done because someone requested it. You can specify who had the request using the genitive or 'von' (of/from).
Auf Wunsch des Gastes wurde das Frühstück auf dem Zimmer serviert.
At the guest's request, breakfast was served in the room.
interest
'das Interesse' and 'der Wunsch' can both express that someone wants something. But 'Interesse' often means that you are curious or want to engage with something. It can also mean that you would like to buy, do, or get to know something more closely. 'Wunsch' is more direct: you hope that something will happen, or you state specifically what you want to have or receive. They are especially easy to confuse with offers. 'Ich habe Interesse an der Wohnung' (I am interested in the apartment) sounds like: I want to know more about it or perhaps rent it. 'Mein Wunsch ist eine ruhige Wohnung' (My wish is a quiet apartment) describes more exactly what you have in mind.

Beim Termin im Bürgerbüro nennt Luis seinen Wunsch nach einem neuen Pass.
At the appointment at the citizens' office, Luis states his wish for a new passport.
Am Morgen zeigt der Fahrer Interesse an der neuen Route.
In the morning, the driver shows interest in the new route.