apple watch
do you need cellular on your Apple Watch to listen to music without your phone nearby?
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Listen to music, podcasts, and audiobooks on your Apple Watch
https://support.apple.com/en-us/HT204691
Play music on Apple Watch
https://support.apple.com/guide/watch/play-music-apd70768b20b/watchos
Add music to Apple Watch
https://support.apple.com/guide/watch/add-music-apd483798d11/watchos
TL;DR - If you store music, podcast or audiobooks on the Apple Watch you can listen to them offline.
You can do this with your own music, or there are some services, such as Pandora that allow you to download an offline playlist and transfer that to your Apple Watch.
You ONLY need a cellular connection if you want to live stream music. Not all streaming services support the Apple Watch. Apple Music, Pandora, and I think Spotify recently joined the list.
The GPS only Apple Watch can do Everything the cellular model can do as long as your iPhone is nearby, where nearby is somewhere in the same 3-4 bedroom home (assuming typical wood frame construction).
https://support.apple.com/en-us/HT205547
The Cellular Apple Watch allows you to leave your iPhone at home while you go for a walk, run, bike ride, etc...
The Cellular Apple Watch shares the iPhone's phone number. This requires the iPhone cellular carrier to support the Apple Watch. The iPhone carrier charges a monthly fee for this service. In the U.S. the fee is $10 per month added to your iPhone bill.
iPhone Cellular Carriers that support the Apple Watch, which models, the radio frequencies each model uses, and the country where they offer service: