The reporting section will tell the number of "resolved" tickets, but that number includes closed. Since there was a felt need to have both resolved and closed as the type of ticket, I feel that the reporting should either accurately reflect only resolved, or it should indicate that it's both.
We resolve a ticket only when the issue/request is fixed/completed. If it wasn't, but the ticket is no longer needed for any reason, we use closed. It will skew metrics to have the "resolved" number include both closed and resolved tickets.