What I have found in looking things back up with the limited time I have to do it in today is this:
And this. (Link jumps you into the middle of the thread. Scroll up to the top, then read back down.) :
About halfway down in the first link, you will find a chart with RN float sizes. IIRC, US sizes were similar, but not identical. Have not been able to find the US sizes in a quick search.
The second link mentions that there were the original--copper cored--Carley floats, and approximately mid-war, the USN came out with pure balsa floats, since copper was a valuable war commodity needed more urgently for other things. Again going by a dim memory, I believe I recall reading that only the US switched to balsa floats. The RN continued to make the copper ones throughout the war. This link also gives the sizes for balsa floats.
One aspect of all this which I remember very clearly is that the US started by just copying the Carley oval shape with the first-production balsa floats. However, those were oval because it was easy to bend the copper ring to that shape. Woodworkers using balsa quickly figured out it was easier to make square corners, rather than trying to make the floats rounded. So, an oval shaped float will either be copper cored, or an early pattern balsa float. The square ones are balsa. The square balsa began to show up in about mid-1943. Since the RN continued with copper throughout the war, you then mainly find square floats only on US ships, and from mid-1943 (or so) onward.
The RN did have a small square float of their own, not to be confused with the US floats. It was called the Denton Raft. Mention and some photos at the bottom of this article here:
IIRC, those had only one size (??)