
die Beziehung
relationship
A romantic and often committed partnership between two people.
Nach fünf Jahren endete ihre Beziehung.
After five years, their relationship ended.
relationship / connection
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relationship
A romantic and often committed partnership between two people.
Nach fünf Jahren endete ihre Beziehung.
After five years, their relationship ended.

relationship / connection
A general relationship or connection between people, groups, things, or circumstances.
Es gibt eine enge Beziehung zwischen der Wirtschaft und der Politik eines Landes.
There is a close relationship between a country's economy and its politics.

to have connections
In the expression 'Beziehungen haben' (to have connections): to have useful contacts with influential people that one can use to one's own advantage.
Er hat den Job nur bekommen, weil sein Vater gute Beziehungen hat.
He only got the job because his father has good connections.
'Beziehung' (relationship / connection) is derived from the verb 'sich beziehen auf' (to refer to). It describes how two or more things, people, or ideas are connected to one another or relate to one another.
Ich verstehe die Beziehung zwischen diesen beiden Ereignissen nicht.
I don't understand the relationship between these two events.
The connection to a person or thing is expressed with 'zu' (+ dative). The connection between two or more elements is described with 'zwischen' (+ dative).
Er hat eine sehr gute Beziehung zu seinen Eltern.
He has a very good relationship with his parents.
In the plural, 'Beziehungen' (connections) can have a special meaning: useful contacts with influential people. The expression 'Beziehungen haben' (to have connections) means that you gain advantages through personal contacts.
Er hat die Stelle nur durch seine Beziehungen bekommen.
He only got the position through his connections.
When referring to a romantic partnership, 'Beziehung' (relationship) is often used with verbs such as 'anfangen' (to start), 'eingehen' (to enter into), 'führen' (to have/maintain), or 'beenden' (to end).
Sie haben beschlossen, ihre Beziehung zu beenden.
They decided to end their relationship.
ribbon / band
Das Band figuratively emphasizes the close emotional connection between people. Die Beziehung refers more generally to the relationship itself and can also mean a romantic partnership, depending on the context. Band is suitable for the closeness that connects people, while Beziehung is more appropriate for the type of relationship.

Nach vielen gemeinsamen Erlebnissen führen Lena und Tom nun eine feste Beziehung.
After sharing many experiences, Lena and Tom are now in a committed relationship.
Die gemeinsamen Erlebnisse haben ein enges Band zwischen Lena und Tom geschaffen.
Their experiences together created a close bond between Lena and Tom.