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.

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 play / happen
'abspielen' and 'spulen' are clearly opposed when talking about audio or video files. With 'abspielen' (to play), the recording runs normally so that you hear or see the content. With 'spulen' (to fast-forward / rewind), you move quickly forward or backward and skip over parts. The words can be confused because both happen with the same medium, for example with a video or an audio file. Memory tip: 'abspielen' means to watch or listen normally; 'spulen' means to go quickly to another point.

Bei der langen Werbung spult Paul ein Stück vor.
During the long ad, Paul fast-forwards a bit.
Nach dem Unterricht spiele ich die Lernaufnahme noch einmal ab.
After class, I play the learning recording again.