The chairs made by these Clissett and Gardiner only look similar at first glance - there is a reasonable range of easy-to-spot difference. In an attempt to help, buyers as much as sellers, I've written a guide distinguish between the two. It's downloadable from the "Ladderback chairs" page, but you can try it out from here, too. Please try it out and let me know if there are any problems.
The chairs in the photograph are by Edward Gardiner. Even with a small blurry photograph like this period one, I can see that the side chair is not by Clissett. This is because the front feet are plain; Clissett's side chair had small ball turnings. With a chair in the hand, there are more than ten features that will help you tell the difference.
With regard to Gimson being designer, not only is there no evidence for that, but it's not a logical conclusion. The Clissett ladderback, already installed as the chair of choice at the Art Workers' Guild, was what inspired Gimson to go an work with Clissett to learn about chairmaking. He clearly had a lot of respect for Clissett, and it's very unlikely that he would have designed an essentially identical chair and manufactured it in competition with his friend. My view is that, after the death of both Clissett and Gimson, Edward Gardiner started making his version of what he called "The Clissett" to satisfy a continuing demand. If anyone has any evidence to the contrary, I'd be very pleased to hear about it - please contact me.