Fangen vs. auffangen
While both fangen and auffangen translate to catching an object in flight, they describe different types of motion and intent. The word fangen is the general term for catching a moving object, such as a thrown ball. In contrast, auffangen implies intercepting an object that is falling downward, usually to prevent it from hitting the ground, breaking, or getting lost.
Fangen
This is the standard and most general verb for catching an object in flight. It is used when an object is actively moving through the air, such as when it is intentionally thrown to someone across a distance, and the person successfully grasps it.
Wirf mir den Ball zu, ich werde ihn fangen.
(Throw the ball to me, I will catch it.)
Der Torwart konnte den harten Schuss problemlos fangen.
(The goalkeeper was able to catch the hard shot without any problems.)
Die Kinder spielen am Strand und fangen den Frisbee.
(The children are playing on the beach and catching the frisbee.)
Du musst den Schlüssel fangen, den ich dir aus dem Fenster werfe.
(You need to catch the key that I am throwing to you out of the window.)
Der schlaue Hund springt hoch, um den fliegenden Stock zu fangen.
(The smart dog jumps high to catch the flying stick.)
Auffangen
This verb specifically describes catching an object that is dropping or falling downwards. It carries a strong nuance of intercepting a downward trajectory to rescue an object, act as a safety net, prevent damage, or collect a falling substance.
Das teure Glas fiel vom Tisch, aber ich konnte es gerade noch auffangen.
(The expensive glass fell off the table, but I was just able to catch it.)
Das große Netz unter dem Trapez soll die Artisten auffangen, falls sie stürzen.
(The large net under the trapeze is meant to catch the artists in case they fall.)
Wir stellen einen Eimer nach draußen, um das viele Regenwasser aufzufangen.
(We are putting a bucket outside to catch the heavy rainwater.)
Das kleine Baby stolperte plötzlich, doch der aufmerksame Vater konnte es rechtzeitig auffangen.
(The little baby suddenly stumbled, but the attentive father was able to catch it in time.)
Sie ließ ihr Handy fallen und versuchte reflexartig, es mit dem Fuß aufzufangen.
(She dropped her phone and reflexively tried to catch it with her foot.)
Summary
To choose the correct word, look at the direction and nature of the object's flight. Use fangen for a normal catch, such as receiving a ball or a frisbee thrown across a horizontal distance. Use auffangen when you need to intercept a falling object to rescue it before it crashes into the floor.