
spulen
to wind
To wind yarn, wire, film, or tape onto a cylindrical roll (spool).
Die Maschine spult den Faden automatisch auf die kleinen Rollen.
The machine winds the thread automatically onto the small rolls.
to wind / to fast-forward
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to wind
To wind yarn, wire, film, or tape onto a cylindrical roll (spool).
Die Maschine spult den Faden automatisch auf die kleinen Rollen.
The machine winds the thread automatically onto the small rolls.

to fast-forward
To move quickly forward or backward through a medium such as a video cassette, film, or audio file without playing it at normal speed.
Spul mal bitte bis zu der Szene, in der sie sich zum ersten Mal treffen.
Please fast-forward to the scene where they meet for the first time.
The verb 'spulen' (to wind / to fast-forward) is derived directly from the noun 'die Spule' (spool). A spool is a cylindrical object onto which you wind something, such as a thread or a cable.
Für die Nähmaschine muss ich zuerst neuen Faden auf eine leere Spule spulen.
For the sewing machine, I first have to wind new thread onto an empty spool.
The meaning is usually clear from the object of the sentence. If thread, yarn, or wire is mentioned, it is about winding. If it is about films, music, or videos, it means moving quickly forward or backward.
Die große Maschine spult den Kupferdraht auf die Rollen.
The large machine winds the copper wire onto the rolls.
In the media meaning, 'spulen' (to fast-forward/rewind) is very often used with the separable prefixes 'vor-' and 'zurück-'. 'Vorspulen' means to fast-forward, and 'zurückspulen' means to rewind.
Kannst du bitte zum Anfang des Liedes zurückspulen?
Can you please rewind to the beginning of the song?
The term comes from the era of cassettes and videotapes. Today, however, 'spulen' (to fast-forward/rewind) is also used for digital media such as videos or podcasts, even though there is no longer a physical spool there.
Spul im Podcast mal zu Minute 15:30.
Fast-forward to minute 15:30 in the podcast.
to wrap / change
Wickeln is the broader term and can describe forming a cable or thread into a roll. Spulen more specifically means winding yarn, wire, or tape onto a cylindrical spool. When the spool is important, spulen is the better choice.

Nach der Arbeit spult sie den Draht ordentlich auf eine zylindrische Rolle.
After work, she neatly winds the wire onto a cylindrical spool.
Nach der Arbeit wickelt sie das Kabel ordentlich zu einer Rolle.
After work, she neatly coils the cable into a roll.