@JTRTech is correct. Paid is a value for a Ticket State named “Status”, while IsClosed is a special flag in the Database that prevents changes to the Ticket.
It just so happens that when a Ticket is fully Paid, both the Ticket “Status” State is set to Paid and the Ticket is Marked as Closed, so it might seem at first that they are the same thing, but in fact they are completely different. In general, it makes sense to Mark the Ticket as Closed when it is fully Paid, so that is why this is a Default Rule that is installed with a fresh Database.
It is important to note that the Close Ticket Action is not the same as the Mark Ticket As Closed Action.
The Close Ticket Action simply removes the Ticket from the POS Screen and changes some Order States (Status=Submitted), Entity States (Status=New Orders), and Ticket State (Status=Unpaid).
The Mark Ticket As Closed Action sets a flag in the Database which prevents altering of the Ticket in any way, and as JTRTech mentions, this flag is reversed via the Reopen Closed Ticket Action. It has nothing to do with States or anything like that. It is somewhat like the Lock Ticket Action, except it is supposed to serve a more special purpose.
In fact, in my Setups, where we would normally Lock the Ticket by default, I removed that Action because I didn’t like it, which is why the IsLocked column is always 0 in my DB…
