Open means that the case is being actively worked.

Closed means that the case is finished, and no more work is being done. Cases with a closed status will not show up in the list of cases when creating new tasks.

Closed (Withdrawn) means that the case is finished, and that you withdrew from it. No more work is being done. Cases with a closed status will not show up in the list of cases when creating new tasks.

Pending (not started) means that the case is open, but work has not yet started, generally due to something outside of your control.

On Hold (open, but paused) means that the case is open, but is not actively being worked. This could be the case if the client has run out of money and needs time to replenish their trust (or pay existing bills) before new work can begin.