It's about when your friends were last signed-in in their account. From my understanding:
Invisible = Sign-in but do not broadcast the games you are playing (though your profile will show that you signed-in)
Offline = Stay offline and do not sign-in
Incorrect. "Invisible" is a privacy control, not just a UI filter. While the official client freezes the text, the backend still broadcasts live last_logon and last_logoff Unix timestamps in the ClientPersonaState packet. This leaks exact real-time sleep/wake cycles via the socket, completely bypassing the privacy toggle.