Well on facebook you could originally choose who you wanted to share things with. Not sure if that's still there because I haven't used it in years.
In theory you could do this with facebook but the defaults matter and they defaulted to sharing very widely. With chat it's obviously and understandably bounded (at least unless a member of the group takes a positive action to forward/copy messages elsewhere, which is not generally very socially accepted to do without some level of permission or least a good reason).