If I recall correctly, Moderna is the one that uses outside contractors in their production process. Unlike Pfizer and J&J, they dont have the capacity to produce everything in house. This has results in some quality control issues. Someone can correct me if I am off base here.
Then Lonza ships it to a “fill and finish” facility to put it in the little vials distributed to pharmacies around the US.
I know someone who works at Lonza. Lonza is a multinational corporation headquartered in Switzerland. The make drugs for all sorts of patent holders including Pfizer, J&J, Merck, Bayer, pretty much everybody.