Connected objects are something WHERE the service should track for new comments/messages - basically it's a link to a social community, an advertising post or account.
Rules are used to organize and manage Connected Objects and their behaviours. Rules decide WHAT TO DO with comment/messages alerts. They determine where to send alert notifications, the frequency of alerts delivery, and control what is filtered into or out of the alerts themselves.
Also please note, that every account in Chotam has at least one default set of Rules to which all Connected Objects are assigned by default, but you can change that. You can create as many Rules as you like.