Like Airplay, Sonos is wifi-based. However, there are some advantages.
Here are what I consider to be the two main ones:
1. Unlike Airplay speakers, Sonos speakers are able to directly connect to cloud and NAS-based music sources. So if you are streaming from something like Spotify or a radio station, or a music folder on a NAS device, Sonos speakers connect directly to them, and the Sonos app on your phone just acts as a controller (rather than a middle-man in the streaming path). With Airplay, the source first gets streamed to your phone or computer (which is acting as a middle-man) and then onto the Airplay speaker. Removal of the middle-man device theoretically at least improves reliability and also means that your phone/computer does not need to stay switched on or remain in your network for the speakers to continue streaming. Perhaps worth noting that Google Chromecast devices operate similarly to Sonos in this regard. It's a more elegant approach then Airplay in my opinion. But if you never stream from internet sources or from network-attached-storage, the benefit here is moot.
2. Wireless linking and mesh networking
Sonos speakers shine when you have more than one of them. They can be wirelessly linked together to form stereo pairs, home theatre setups, and room and floor zones and are kept in perfect synchrony (which is apprarently very hard to do wirelessly). Reliability is also enhanced by the formation of a mesh network for speaker-to-speaker communication which operates on its own wifi channel separately from the home wifi netork. I have difficulties with my home wifi network, but I never have reliability issues with my Sonos speakers and I attribute this to the dedicated mesh network they create.
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I don't use Apple Music so not sure what the issue is here, but there must be a simple solution.
I use Google Music to store my personal music and all I do is link Sonos to my Google Music account and my whole library is available to me from the Sonos app.