Preface: I forgot about the GTD, however it's not immediately clear whether it's actually a factory vehicle. So to just be up front, I'm not sure if it counts or not but I admit it could count.
Anyway, it's mixed. There are factory Shelbys from Ford, which are the "standard" Shelbys, known as SVT Shelbys. However, separate upfitters do the work for certain packages. Roush and Saleen do their upfitting in their houses, which is why they're separate. They take a complete factory Ford, then modify it to their spec. Similarly, I know (at least, up until 2018 when I was looking at window stickers), those Shelby F-150s are 3rd-party upfitted with licensed parts. It's the same place that did the Black Ops F-150 and I forget what other gig they did. That Shelby website doesn't make it clear, but I'm 99% sure all of them are packages you can buy to upgrade your plain Ford Mustang. They're licensed GT350 kits, as opposed to factory GT350s. I know it sounds ridiculous to be so pedantic, but it's a nuance that has to be applied when reporting what manufacturers are officially building. 3rd-party upfitters are not held to nearly as many EPA and crash regulations as the original manufacturer.
The difference is whether the complete vehicle shipped out the Ford factory door directly to a dealer or if it went to a separate upfitter as a complete vehicle, then got modified. Both can still go to a Ford dealer for sale as a new car. Roush/Saleen will have the original window sticker on the door and an upfitter window sticker/addendum added. Roush has a full size sticker on the windshield, for example.