Explicit placement and partitioning of chats

I'm confused by the use of the chat plugin. I see that it can be placed in the bottom corner. But I'm not sure who is involved in that chat. If 10 users all enter the bottom corner chat, are they all in the same chat room? What if they enter the bottom corner chat from different posts or pages? Is there one chat room per page/post, or is there a single one for all bottom corner chats?

I'm more interested in using chats on specific pages dedicated to specific topics. I expected to use a shortcode to place a chat on a page, but I don't see any reference to that, which makes me think that chats will appear on every page and post. That's not what I want, anyway, but I don't understand who is involved in each chat. Is there simply a large chat room for the entire site, or is there a chat room per page/post?

What I'm looking for is multiple private chat rooms based on certain topics. Let's say we're talking about games. So, I want to have one chat room for chess, one for checkers, one for bridge, etc. And tic-tac-toe is so simple that I don't want to put a chat room in that area.

Will the chat plugin accomodate that kind of setup? If so, how do I accomplish that? If not, what can it do?

Is there some documentation somewhere that I'm missing, because this all seems pretty fundamental, but I can't find it anywhere.