Closing/Open inventory question

Hi
Sorry if this is a stupid question but I am confused.

When calculating cost of sales in marginal costing..

the proforma I have learnt is

variable cost of sales=
+variable production costs
+opening stock
– closing stock

etc etc..

However when working on the topic budgeting. To work out a production budget the proforma is

Sales
+closing inventory
-opening inventory

= production quantity.

I know both examples are different and calculating two seperate things but Why is in that in the MC proforma when calculating COS we -closing inventory and + open inventory, but in the budgeting topic when calculating production budget we +closing inventory and – open inventory?

Can you help me by explaining the logic behind both.

This might be going back to basics but I am confused and it in causing confusion.

Thanks