No, there is no rim on the cap... the "rim" is just the base of the hood itself.
As I mentioned, this type of cap was also used on the Nikon RF hoods. They make a nice compact unit, and protect the threads of the hood. I use one on a Nikon 135/3.5, with a Leica/Canon mount, and it looks and works very nice.
I have examples of the 34 and 48mm caps, but haven't been lucky enough to find one of the 40mm, as yet.
The body caps can be found in metal, with Canon and Japan in 2 lines at the rim, and in plastic/bakelite (?) in black, plain front, with Canon and Japan in 2 lines, centered as the hood caps, on the inside. I imagine there are variations produced over the years, as there are for so many of the small Canon collector items. Makes life interesting......
I've included photos to show the items clearer. First shows inside of plastic cap and outside of metal one, with hood cap below. Second pic shows the other sides of the items. Note the flat black painted interior of both the metal caps.
The metal body caps are also rather tough to find, and you seldom see them on the auctions. For pure protection, go with the unmarked metal body caps sold by a couple of different vendors on eBay. Check prices, as they seem to be the same items, but price can vary by several $$. You can also buy a nice hood or two to reduce the shipping cost per item. There are some nice ventilated hoods that work well and are priced to sell. No relationship with vendors, except as a satisfied customer.
Harry
Harry