der Falke
falcon
A fast bird of prey with pointed wings, known for its hunting abilities.
Ein Falke stieß aus großer Höhe auf seine Beute herab.
A falcon swooped down on its prey from a great height.

falcon / hawk
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falcon
A fast bird of prey with pointed wings, known for its hunting abilities.
Ein Falke stieß aus großer Höhe auf seine Beute herab.
A falcon swooped down on its prey from a great height.

The political meaning is a metaphor. A 'Falke' (hawk) is a person who takes a hard, aggressive, and uncompromising stance, similar to the bird of prey when hunting.
In der Debatte über die Zinserhöhung setzten sich die Falken durch.
In the debate about the interest rate increase, the hawks prevailed.
This term is used almost exclusively in discussions about politics and economics. Typical topics are monetary policy (central bank), foreign policy, or security issues.
Der Außenminister gilt als Falke in der Sicherheitspolitik.
The foreign minister is considered a hawk in security policy.
When referring to the bird, 'der Falke' (the falcon) is often combined with verbs and phrases such as 'am Himmel kreisen' (to circle in the sky), 'Beute jagen' (to hunt prey), or 'vom Himmel stoßen' (to dive/swoop down from the sky).
Wir beobachteten, wie ein Falke hoch über dem Feld kreiste.
We watched a falcon circling high above the field.
The words 'der Falkner' (a person who hunts with or trains falcons) and 'die Falknerei' (the art of hunting with falcons) are derived from the word 'Falke' (falcon).
Im Mittelalter war die Falknerei ein beliebter Sport des Adels.
In the Middle Ages, falconry was a popular sport among the nobility.
eagle
'der Adler' and 'der Falke' are both birds of prey, so they can easily be confused. An eagle is a large, powerful bird with strong talons. A falcon is usually smaller and is especially known for its fast hunting flights. In nature, 'Adler' fits better when the bird looks large and powerful. 'Falke' fits when you mean a fast bird of prey with pointed wings.

Plötzlich stürzte ein Falke schnell auf seine Beute herab.
Suddenly, a falcon quickly swooped down on its prey.
Der Adler saß ruhig auf einem hohen Felsen.
The eagle sat calmly on a high rock.