longing
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longing
A strong, often painful desire for a person, place, thing, or state that is distant or unreachable.
Nach Monaten im Ausland hatte sie große Sehnsucht nach ihrer Familie.
After months abroad, she had a great longing for her family.
The word is made up of 'sehnen' (to yearn) and 'Sucht' (addiction). This shows the intensity of the feeling: it is a desire that can be almost like an addiction.
Ihre Sehnsucht nach dem Meer wurde jeden Tag größer.
Her longing for the sea grew greater every day.
'Sehnsucht' (longing) is almost always used with the preposition 'nach' (for/after) and the dative. The pattern is: Sehnsucht nach jemandem/etwas haben (to have a longing for someone/something).
Er hat große Sehnsucht nach seiner Heimatstadt.
He has a great longing for his hometown.
Common verbs used with 'Sehnsucht' (longing) are 'haben' (to have), 'verspüren' (to feel), or 'fühlen' (to feel). The feeling is often described with adjectives such as 'groß' (great), 'tief' (deep), or 'schmerzlich' (painful).
Manchmal verspüre ich eine tiefe Sehnsucht nach der Stille der Natur.
Sometimes I feel a deep longing for the silence of nature.
wish
'der Wunsch' and 'die Sehnsucht' both describe that someone would like something or longs for something. 'Wunsch' is more neutral and can be small or big, for example a gift, a day off, or a certain result. 'Sehnsucht' is much stronger and more emotional. It is especially fitting when something is far away, hard to reach, or lost, for example a person, home, or an earlier state. You can use 'Wunsch' very often in everyday life. You use 'Sehnsucht' when the feeling is deep and often also hurts a little.
Wegen der langen Reise hatte Tom große Sehnsucht nach zu Hause.
Because of the long trip, Tom had a strong longing for home.
Annas Wunsch ist, dass ihre Familie am Sonntag zusammen isst.
Anna's wish is for her family to eat together on Sunday.