On Unix, there was the "talk" command for split-screen chat, and also "write" to just send a message to someone else's terminal subject to permission with the "mesg" command. Not all systems had such provisions (or, in come cases, they had to be written by users).
talk, or later ntalk in Unix. Or wall to send to everyone. I used a system in the 80's (Pick DB) that had a send-message command. Also tandem which allowed you to take over someone's terminal like screen-sharing now. If you were the super-user you could do it without asking for permission, and start typing messages to the unlucky user..