I'll use food manufacturing plant I worked at as an illustration:
1. A production department produced the item - measuring, slicing, dicing, baking, mixing, frying, what have you. Production happens on-site.
2. Packaging involves portioning and sealing the item into a container, putting those containers into boxes, and palletizing the boxes so forklifts can move them about. Packaging happens on-site.
3. Distribution happens almost exclusively in a warehouse: taking product from the packagers, and dumping production lots in a warehouse. Then they picking individual boxes of products from one pallet and re-palletizing many different products into into individual orders for shipment. Distribution happens on-site.
4. Shipment is where they take a warehoused order, load it into a vessel (train, boat, truck, aircraft, etc), moving the vessel, and then unloading the vessel at either another warehouse, or a point of sale. Shipment by definition, touches sites, but is otherwise off-site.
They're utterly distinct, and have well-defined interfaces.
There are two ways to parse it (parenthesis added for clarity - I hope)
1. (Packaging for Shipment) and (Distribution)
2. Packaging (for Shipment or Distribution).
In any event, let's got with the way that the businesses hope to save money:
- "packaging for shipment" is just that - packaging inside a factory.
- "distribution" involves the folks working in a warehouse.
Shipping (and the truckers suing for overtime) on the other hand, have a good argument: shipping is not distribution.