I have a little different take on this pan and the process to make it.
In my mind the word machined here means that the metal has been mounted in a lathe and formed. I don't believe any cutting or removal of metal is happening in the machining.
I also think the term spun is referring to forming metal through metal spinning. That is the mounting of a metal blank, could be sheet metal, wrought iron sheet or some other metal on a lathe. The blank would then be spun up and shaped around a mandrel that was also mounted on the lathe with a series of roller tools, either hand applied or by automated methods.
If they are saying the pan is iron, it would be wrought iron in my mind.
If you look at the pictures in the link to the Netherton works you can see a gentleman spinning a piece.
Centrifugal casting is interesting in that the mold is usually spinning with the metal poured into the middle. It is flung out to the edges of the mold and cools from the outside edge in. Makes nice big cylinders for the most part (think cast iron water pipe for instance.
I've attached a couple pictures.
One other think I've thought about regarding cast and wrought iron and steel is that iron has lots of carbon in it, steel has quite a bit less.
Just my interpretation.
Tom
p.s. Here's a link to an Australian metal spinning website video area. Start with the introduction and let it run. It ought to make you smile.
http://southernmetalspinners.com.au/reviews/