Offline on ps4? - 1

I would be interested to know why on PlayStation 4 there's sometimes a red circle with a white x inside for offline people and why sometimes just a white box. I first thought that those who went offline have the cross and those who are offline have the box but somehow it is not so.

The white box is said to be a cell phone. Means they are offline, but can be reached via the app.

At least that's what I assume.