die Berührung
touch
Direct physical contact between two or more people, body parts, or objects.
Eine sanfte Berührung an der Schulter kann mehr Trost spenden als viele Worte.
A gentle touch on the shoulder can offer more comfort than many words.

touch / contact
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touch
Direct physical contact between two or more people, body parts, or objects.
Eine sanfte Berührung an der Schulter kann mehr Trost spenden als viele Worte.
A gentle touch on the shoulder can offer more comfort than many words.

'Die Berührung' (touch/contact) is the noun derived from the verb 'berühren' (to touch). It describes the action or result of touching.
Bitte berühren Sie die Ausstellungsstücke nicht.
Please do not touch the exhibits.
The figurative meaning is used almost exclusively in the fixed expression 'mit etwas/jemandem in Berührung kommen' (to come into contact with something/someone). This construction requires the dative.
In meinem Beruf komme ich mit vielen verschiedenen Kulturen in Berührung.
In my job, I come into contact with many different cultures.
The fixed expression 'in Berührung kommen mit' (to come into contact with) signals the figurative meaning. If 'Berührung' (touch/contact) stands alone or with adjectives like 'sanft' (gentle) or 'kalt' (cold), it usually means direct physical contact.
Er war noch nie mit dem Gesetz in Berührung gekommen.
He had never come into contact with the law before.
In the literal sense, 'Berührung' (touch/contact) is often combined with adjectives that describe the type of contact, e.g. 'eine sanfte Berührung' (a gentle touch), 'eine flüchtige Berührung' (a fleeting touch), or 'eine zärtliche Berührung' (a tender touch).
Eine flüchtige Berührung ihrer Hände reichte aus, um ihn nervös zu machen.
A fleeting touch of their hands was enough to make him nervous.
closeness / proximity
'die Nähe' and 'die Berührung' both have to do with contact. However, 'Nähe' usually means that someone or something is not far away. This can be spatial, but also emotional: you feel close to a person. 'Berührung' means direct contact, for example when a hand touches an arm. In the expression 'mit etwas in Berührung kommen' (to come into contact with something), it can also mean that you have an experience with something. The words can be confused because closeness can often lead to touch. But closeness is not yet direct contact; touch is.

Die Berührung der heißen Pfanne tat sofort weh.
Touching the hot pan hurt immediately.
In der Nähe der Bibliothek gibt es einen kleinen Supermarkt.
There is a small supermarket near the library.