
der Abschuss
shootdown
The hitting and destroying of a flying object, especially an aircraft or a missile, with a weapon.
Der Abschuss der feindlichen Drohne wurde vom Kommando bestätigt.
The shootdown of the enemy drone was confirmed by command.
shootdown / killing / rejection
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shootdown
The hitting and destroying of a flying object, especially an aircraft or a missile, with a weapon.
Der Abschuss der feindlichen Drohne wurde vom Kommando bestätigt.
The shootdown of the enemy drone was confirmed by command.

killing
The killing of a wild animal with a shot as part of hunting.
Der Jäger erhielt die Genehmigung für den Abschuss eines Rehbocks.
The hunter received permission for the killing of a roebuck.

rejection
Colloquial for a clear rebuff or rejection, especially during a romantic or social attempt to approach someone.
Er hat sich bei seiner Traumfrau einen totalen Abschuss geholt.
He got totally rejected by the woman of his dreams.
'Der Abschuss' (shootdown / killing / rejection) is the noun for the separable verb 'abschießen' (to shoot down / to shoot). The verb means to hit something with a shot, bring it down, or kill it.
Der Soldat hat befohlen, die Rakete abzuschießen.
The soldier ordered them to shoot down the missile.
You can recognize the meaning from the topic: in a military context, it is about flying objects; in a hunting context, about animals; and in a social, colloquial context, about a rejection.
Der Abschuss des Satelliten wurde weltweit kritisiert.
The shootdown of the satellite was criticized worldwide.
The meaning 'rebuff' or 'rejection' is strongly colloquial. Use this expression only in informal conversations with friends.
Ich habe versucht, sie nach einem Date zu fragen, aber ich habe mir einen totalen Abschuss geholt.
I tried to ask her out on a date, but I got totally rejected.
In the colloquial meaning, the fixed expression 'sich einen Abschuss holen' (to get rejected) is almost always used. The person who is rejected is the subject of the sentence.
Er hat auf der Party bei drei verschiedenen Frauen versucht zu flirten und hat sich jedes Mal einen Abschuss geholt.
At the party, he tried to flirt with three different women and got rejected every time.
to shoot dead
When a wild animal is killed with a shot, both words can fit. Erschießen generally describes the method of killing with a firearm, while Abschuss refers to the action from the perspective of hunting and the hunted animal. Use erschießen for the process and Abschuss as the hunting term.

Der Jäger meldete den Abschuss des Wildtiers.
The hunter reported the killing of the wild animal.
Der Jäger erschoss das Wildtier mit einem Schuss.
The hunter shot the wild animal dead with a single shot.