der Tanz
dance
The movement of the body to music, often following a specific rhythm or choreography.
Der Tanz des Paares war elegant und ausdrucksstark.
The couple's dance was elegant and expressive.

dance
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dance
The movement of the body to music, often following a specific rhythm or choreography.
Der Tanz des Paares war elegant und ausdrucksstark.
The couple's dance was elegant and expressive.

The noun 'der Tanz' (dance) is the nominalization of the verb 'tanzen' (to dance). It describes both the action and the result of dancing.
Tanzen ist ihr liebstes Hobby.
Dancing is her favorite hobby.
The phrase 'jemanden zum Tanz auffordern' (to ask someone to dance) is a fixed expression and means to ask someone whether he or she would like to dance with you.
Er war zu schüchtern, sie zum Tanz aufzufordern.
He was too shy to ask her to dance.
In a figurative sense, 'der Tanz' (dance) describes a complicated, difficult, or nerve-racking process. The phrase 'ein Tanz mit...' (a dance with...) is typical here.
Die Verhandlungen waren ein langer Tanz mit vielen Kompromissen.
The negotiations were a long dance with many compromises.
When 'Tanz' (dance) refers to a specific choreography or performance, it is often combined with verbs like 'lernen' (to learn), 'üben' (to practice), or 'aufführen' (to perform).
Die Kinder führen bei der Schulfeier einen Tanz auf.
The children are performing a dance at the school celebration.
When referring to a dance event, prepositions like 'zum' or 'auf dem' are often used. 'Zum Tanz gehen' means to attend a dance party.
Wir gehen am Wochenende auf den Tanz in der Stadthalle.
We're going to the dance at the town hall this weekend.
ball
'Ball' and 'Tanz' can both have to do with music, movement, and an event. A 'Ball' is usually a large, festive, and rather formal dance event. 'Tanz' mainly means movement to music, but it can also mean an event or a specific type of dance such as a waltz or tango. That is why the words can be confused when talking about an event. If the celebration is elegant and official, 'Ball' fits better. If you are talking about the movement, the steps, or a type of dance, 'Tanz' is more precise.

Im Kurs üben wir heute einen schnellen Tanz für die Feier.
In the course, we are practicing a fast dance for the celebration today.
Zum Abschluss der Schule findet im Juni ein großer Ball statt.
A big ball will take place in June to mark the end of school.