We had both aspects. Even on Usenet, some groups were so active and internet-connected that you would see the threaded discussion exploding around you in the minutes it took to write a reply. Others were more like putting a message in a bottle and checking back each day to see if a reply was floating back.

In university, I also remember we had informal protocols for upgrading a conversation from email or newsgroup to more real time via shared systems on campus. We would use "talk" and "ytalk" to have something more instant than instant messaging... you would see each letter as the other party typed, rather than only seeing one chunk of text per enter key. One student group also used the MOTD on a shared system as a communal bulletin board, hosting elaborate chats a bit like graffiti tags answering each other.