der Ball
ball
A round or oval piece of sports equipment used in many sports and games by throwing, catching, or kicking it.
Die Kinder spielen im Park mit einem Ball.
The children are playing with a ball in the park.

ball
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ball
A round or oval piece of sports equipment used in many sports and games by throwing, catching, or kicking it.
Die Kinder spielen im Park mit einem Ball.
The children are playing with a ball in the park.

Although they are spelled the same, 'der Ball' (ball, sports equipment) and 'der Ball' (formal dance) are two words with different origins. The context, such as sports or a formal invitation, always makes clear which meaning is intended.
Die Kinder kicken den Ball über die Wiese.
The children kick the ball across the meadow.
In the meaning 'Spielgerät' (piece of sports equipment), Ball is used with typical sports verbs. These include: 'einen Ball werfen' (to throw a ball), 'fangen' (to catch), 'treten' (to kick), 'schießen' (to shoot), or 'prellen' (to bounce).
Der Torwart konnte den Ball gerade noch fangen.
The goalkeeper was just able to catch the ball.
When Ball means a dance event, you go 'auf einen Ball' (to a ball) or 'besucht einen Ball' (attend a ball). It is often part of compound words such as Abschlussball (graduation ball/prom), Opernball (opera ball), or Kostümball (costume ball).
Der Abschlussball unserer Schule findet dieses Jahr im Rathaus statt.
Our school's graduation ball is taking place in the town hall this year.
The idiom 'am Ball bleiben' means that you keep going with something in an engaged way. The preposition 'an' requires the dative here.
Das Projekt ist schwierig, aber wir müssen jetzt am Ball bleiben.
The project is difficult, but we have to stick with it now.
soccer / football
'der Fußball' and 'der Ball' can both mean a round piece of sports equipment. 'Ball' is the general word for many sports and games. 'Fußball' is more specific: it is the ball used in a game of soccer. Learners may confuse the words because a soccer ball is always a ball, but not every ball is a soccer ball. If the sport is clear or important, you say 'Fußball'. If it is just about any play ball, 'Ball' fits better.

Im Park hat ein Kind den Ball über den Zaun geworfen.
In the park, a child threw the ball over the fence.
Der Fußball liegt noch auf dem Sportplatz neben dem Tor.
The soccer ball is still on the sports field next to the goal.