How does multi-device implementation work (for the layman). Are the messages only delivered to the 'logged in' clients? So if I am logged in on the desktop my

How does multi-device implementation work (for the layman). Are the messages only delivered to the 'logged in' clients? So if I am logged in on the desktop my message exchanges are also sent to the phone client? But any messages I send/receive from my phone while logged out of my desktop are synced through the server on login?