The two clubs are the Caterpillar Club and the Caterpillar Club Association. I presume the former is just the records held by Irvin (without the 'e' on the end). Although called the Caterpillar Club, and had a membership card it was never a true club as we would know it, IE reunions, committee and the like. I guess this is where the Caterpillar Club Association comes in.
Irvin would not have allowed a badge to be made for anyone, or more accurately engraved for anyone, unless they could verify the details. The procedure was to apply via the CO and then enquiries would begin. If they could verify the circumstances and that it was an Irvin chute being used a member he would become (it might instead have been a GQ or other chute used).
I applied for one as mentioned and 50 odd years later they were able to confirm details. The other man from the same crew got his in 1945 after his CO at the time applied on his behalf.
Payment would normally only be for a replacement badge indicating your Great Grandfather got one and then lost it. He applied for a replacement and as such had the associated costs.