aufzeichnen
to record
To capture audio or video signals on a storage medium so they can be played back later.
Wir sollten das Interview aufzeichnen, damit uns keine Details entgehen.
We should record the interview so we don't miss any details.

to record / note down
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to record
To capture audio or video signals on a storage medium so they can be played back later.
Wir sollten das Interview aufzeichnen, damit uns keine Details entgehen.
We should record the interview so we don't miss any details.

'Aufzeichnen' (to record / note down) is a separable verb. The prefix 'auf-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Journalist zeichnete das gesamte Gespräch auf.
The journalist recorded the entire conversation.
The verb consists of the prefix 'auf-' and the verb 'zeichnen' (to draw). The prefix conveys the idea of capturing information on a surface or medium—whether on tape, on paper, or as an image.
Er zeichnete seine Beobachtungen in einem Notizbuch auf.
He noted down his observations in a notebook.
The object of the sentence reveals the exact meaning. If it refers to technical media (film, conversation, broadcast), it means 'aufnehmen' (to record). With information (data, thoughts), it means 'notieren' (to note down). With visual things (route, plan), it means 'skizzieren' (to sketch).
Ich zeichne die Sendung auf, weil ich später keine Zeit habe.
I'm recording the show because I won't have time later.
In the technical meaning, 'aufzeichnen' is often combined with digital or analog media. Typical phrases are: 'eine Sendung aufzeichnen' (to record a broadcast), 'ein Video aufzeichnen' (to record a video), 'ein Telefongespräch aufzeichnen' (to record a phone call), or 'ein Konzert aufzeichnen' (to record a concert).
Viele Menschen zeichnen ihre Lieblingsserien auf, um sie später anzusehen.
Many people record their favorite series in order to watch them later.
to record / take in
'aufnehmen' and 'aufzeichnen' can be very similar when sound or video is recorded with a device. In this sense, you can often use both words. 'aufnehmen' sounds especially natural in everyday language with a phone, camera, or microphone. 'aufzeichnen' sounds a bit more precise or technical and emphasizes recording something on a storage medium. In addition, 'aufzeichnen' can also mean writing something down, while 'aufnehmen' in official contexts more often means putting a record or data on file. The words are easy to confuse because both save something for later. As a guide: for normal audio and video recordings, 'aufnehmen' is very common; for documentation or more precise recording, 'aufzeichnen' fits well.

Der Lehrer zeichnet die wichtigsten Ergebnisse der Diskussion auf.
The teacher records the most important results of the discussion.
Sie nimmt die Sprachnachricht im Bus auf.
She records the voice message on the bus.