No, they are both Bluetooth receivers.

Thought so. Thank you.

The Sonos speaker seems redundant here.  You should be able to share the music with your phone, and from there to Sonos Ace using Bluetooth. 

If it’s a local library, any player should send across Bluetooth to the Sonos Ace. If it’s a streaming company where the playlist exists, you’d want to use their app. The Sonos app isn’t a ‘player’, so you can’t ‘send’ it through Bluetooth. The Sonos controller is only a remote, to show what is happening on the Era 100 speaker, which ​@jgatie points out, doesn’t ‘send’ a Bluetooth signal. 

Thank you for the replies. It is a local library on a NAS. More research needed from me, I think.

If it is a local library, any ‘player’ on your phone should work.

No need to involve the Sonos app, or the Sonos speaker(s), just use Bluetooth to send the signal from your phone the the Ace headphones. 

Yup, I've got it now. Thanks.