die Distanz
distance
The spatial gap or distance between two points, places, or objects.
Die Distanz zwischen den beiden Städten beträgt ungefähr 200 Kilometer.
The distance between the two cities is about 200 kilometers.

distance
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distance
The spatial gap or distance between two points, places, or objects.
Die Distanz zwischen den beiden Städten beträgt ungefähr 200 Kilometer.
The distance between the two cities is about 200 kilometers.

'Distanz' (distance) is often used with the prepositions 'zu' (to; direction/reference) and 'zwischen' (between; two points). The phrase 'auf Distanz' describes a state of distance.
Bitte halte mehr Distanz zum vorderen Fahrzeug.
Please keep more distance from the vehicle in front.
You can tell from context whether a spatial or emotional distance is meant. If it is about places and measurements (meters, kilometers), it is spatial. If it is about feelings, relationships, and behavior, it is emotional.
Aus dieser Distanz kann ich das Schild nicht lesen.
From this distance, I can't read the sign.
In an emotional or social context, people often talk about 'Distanz wahren' (to maintain distance), 'Distanz halten' (to keep one's distance), or 'Distanz schaffen' (to create distance).
Als Lehrerin muss sie eine professionelle Distanz zu den Schülern wahren.
As a teacher, she has to maintain a professional distance from the students.
The phrase 'auf Distanz gehen' (to distance oneself) is used with the preposition 'zu' + dative to express whom or what one is distancing oneself from.
Er ist nach der Auseinandersetzung zu seinen Kollegen auf Distanz gegangen.
After the confrontation, he distanced himself from his colleagues.
closeness / proximity
'die Nähe' and 'die Distanz' are often opposites. 'die Nähe' means that there is little distance, either physically or emotionally. 'die Distanz' means distance or a reserved, cooler attitude. With places, you can use both as opposites: 'Nähe zum Zentrum' (proximity to the center), 'Distanz zum Zentrum' (distance from the center). With people, 'Nähe' sounds personal and familiar, while 'Distanz' sounds more cautious or distant. Learners may confuse the words because both talk about relationships or distance. Pay attention: 'Nähe' connects, while 'Distanz' separates or keeps distance.

Nach dem Streit ist zwischen Tom und seinem Bruder eine spürbare Distanz entstanden.
After the argument, a noticeable distance has developed between Tom and his brother.
Die Nähe zu ihrer Familie gibt Lena viel Sicherheit.
Being close to her family gives Lena a lot of security.