der Käfig
cage
A container made of bars, rods, or wire that is used to confine or transport animals.
Der Kanarienvogel saß in seinem goldenen Käfig und sang.
The canary sat in its golden cage and sang.

cage
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cage
A container made of bars, rods, or wire that is used to confine or transport animals.
Der Kanarienvogel saß in seinem goldenen Käfig und sang.
The canary sat in its golden cage and sang.

Pay attention to the case after the preposition 'in'. 'Im Käfig' (in the cage; in + dem) describes where something is located (dative), while 'in den Käfig' (into the cage) describes where something is moving to (accusative).
Der Löwe läuft unruhig in seinem Käfig auf und ab.
The lion paces restlessly back and forth in its cage.
When 'Käfig' is used with animals, grates, or bars, the literal meaning is intended. In connection with feelings, relationships, or social situations, the figurative meaning of a restrictive situation is meant.
Der Hamster schläft in seinem Käfig.
The hamster sleeps in its cage.
In the literal sense, 'Käfig' is often used with verbs that describe confinement or keeping something enclosed. Typical examples are 'ein Tier im Käfig halten' (to keep an animal in a cage), 'jemanden in einen Käfig sperren' (to lock someone in a cage), or 'im Käfig sitzen' (to sit/be in a cage).
Es ist verboten, Wildvögel in einem Käfig zu halten.
It is forbidden to keep wild birds in a cage.
The expression 'ein goldener Käfig' (a golden cage) describes a situation in which someone has material wealth and luxury, but loses their personal freedom in return. It is almost always used in the figurative sense.
Sie lebt in einem goldenen Käfig: Sie hat alles, was man kaufen kann, aber keine Freiheit.
She lives in a golden cage: she has everything money can buy, but no freedom.
prison
'das Gefängnis' and 'der Käfig' can both be places where someone or something is locked up. 'Gefängnis' is used for people and refers to an institution or building for offenders. 'Käfig' is usually used for animals and means a container with bars or wire. In a figurative sense, 'Käfig' can also mean a situation in which a person feels very restricted. The words can be confused because both have to do with lack of freedom. For real punishment and the police, 'Gefängnis' fits; for animals or figurative language, 'Käfig' is more likely.

Der Hamster schläft in seinem Käfig unter dem kleinen Holzhaus.
The hamster is sleeping in its cage under the little wooden house.
Vor dem Gefängnis warten die Besucher auf die Kontrolle.
The visitors are waiting outside the prison for the security check.