In Civicase - reports ignore 'Order' on 'Status' and use status id instead?
There is a "weight" field and a "value" field for each status. Changing the ordering on the admin pages changes the weight. Changing the "value" will correspond to status_id, but be careful about that - I'm not sure if it will autoupdate your existing data, i.e. if the value of "Completed" is "2" and you change it to "7", you might still have data in the system that has "2" stored and so it won't represent Completed anymore. You would then need to update civicrm_case.status_id in the database to match. Make a backup first if you're going to try that!

Weight is used for ordering in dropdown lists and such.