einfangen
to catch
To catch an animal that is running around freely and take it into custody.
Die Feuerwehr musste die entlaufene Kuh auf der Weide wieder einfangen.
The fire department had to catch the escaped cow in the pasture again.

to catch / capture
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to catch
To catch an animal that is running around freely and take it into custody.
Die Feuerwehr musste die entlaufene Kuh auf der Weide wieder einfangen.
The fire department had to catch the escaped cow in the pasture again.

'Einfangen' (to catch / capture) is a separable verb. The prefix 'ein-' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Bauer fängt seine entlaufenen Schafe wieder ein.
The farmer catches his escaped sheep again.
You can recognize the meaning from the object: If it is an animal, it means catching. With abstract nouns like 'Stimmung' (mood) or 'Moment' (moment), it is about capturing an impression. The reflexive form 'sich etwas einfangen' (to catch something) always refers to illnesses.
Der Tierpfleger muss den Affen einfangen.
The zookeeper has to catch the monkey.
In the figurative meaning, 'einfangen' (to capture) is often combined with abstract nouns. Typical examples are: 'die Atmosphäre einfangen' (to capture the atmosphere), 'einen Augenblick einfangen' (to capture a moment), or 'ein Lächeln einfangen' (to capture a smile).
Mit seiner Kamera fängt er einzigartige Augenblicke ein.
With his camera, he captures unique moments.
To express that someone gets sick, you use the fixed reflexive structure 'sich (Dativ) etwas (Akkusativ) einfangen' (to catch something). The person is in the dative.
Pass auf, dass du dir bei diesem Regen keine Erkältung einfängst!
Be careful not to catch a cold in this rain!
The expression 'sich eine Krankheit einfangen' (to catch an illness) is colloquial. In a formal or medical context, you would more likely use 'sich anstecken' (to become infected) or 'erkranken' (to fall ill).
Ich glaube, ich habe mir die Grippe eingefangen.
I think I caught the flu.
to record / take in
'aufnehmen' and 'einfangen' can both mean that you preserve a moment, an image, or a sound. 'aufnehmen' sounds more technical and direct: a camera, microphone, or phone saves something. 'einfangen' fits better when it is about a mood, a special moment, or an impression. It often sounds more figurative and personal. So you can 'ein Video aufnehmen' (record a video), but 'die Atmosphäre einer Feier in einem Foto einfangen' (capture the atmosphere of a celebration in a photo).

Das Foto fängt die ruhige Stimmung am Morgen sehr gut ein.
The photo captures the quiet mood of the morning very well.
Auf der Feier hat mein Bruder ein kurzes Video aufgenommen.
At the party, my brother recorded a short video.