Active means action
Keep a ticket active while somebody on the team needs to investigate or reply. An active queue should be a trustworthy list of current work, not a permanent archive.
Pending means waiting
Use pending when the next move belongs to the customer or an external party. Include a clear question or expectation in the last reply so another agent understands the wait.
Closed means complete
Close a ticket when the request is resolved and no follow-up is planned. Reopen or continue it if new information changes the outcome rather than creating disconnected history.