Which one of the two expressions "Process of shipment" and "Process of shipping" seem correct? The NyTimes seems to be using both of them:
Shipment, in the Oxford English Dictionary’s definition, can mean ‘the act of shipping (goods or commodities) for transportation’ and shipping can mean ‘the action of putting persons or things on board ship or transporting them by ship’. So not much difference, but since both imply the act or action of moving stuff around on the sea, the question should perhaps be whether the word process is required as well.
Shipping -> business or act of sending something
Shipment -> cargo or freight
shipping is the process, shipment is the result.
You are shipping the package to someone, when you finish, the shipment will be ready to transport
In my view, 'process of shipping' is correct. A very quick google search on 'process of' seems to indicate that 'process of' is followed by a verb and this is what I would expect in any case. It seems to me that a process is a process of something happening - and that something happening is a verb. Newspapers often use slightly incorrect English which isn't necessarily terrible because English is what we make of it and I think rules can be bent. Having said that, I do think 'process of shipment' doesn't sound quite right anyway. Stick with the verbs in this case :-)
Both are possible but the may differ in meaning depending on context. While shipping denotes "the activity of carrying", shipment will both refer to "act of transporting goods" or "quantity of goods sent".