What I understand Thomas to be saying is the difference between the examples.
AP, Cartier et al hired Gerald Genta to design watches for them. Now they make Genta's designs under their own label but the public is fully aware Gerald Genta designed the watches at the request of the watchmaker. Genta was the contractor hired by the brands to perform a task.
On the other hand, as Thomas tells it, one version of the story is that Jeff Barnes created the designs for the Antiqua, Classic and Trio as you posted, and then recruited Vianney Halter as a watchmaker to execute the designs. But now Vianney Halter is making those watches with no mention of Jeff Barnes at all, so the uninformed it would appear that they were completely Vianney's designs.
- SJX