It's true that the footage of such things sometimes gets mixed up, but I don't know of anyone who has tried to do a study of it. If one goes through the imagery used around the atomic and hydrogen bombs, then and today, one finds lots of misattribution. I suspect it is out of ignorance rather than maliciousness. Certainly the Nagasaki footage is much higher-quality than the Hiroshima footage (it's in color, it's more steadily filmed, it is less damaged). Using an H-bomb's footage is just misleading, but again for most people I am not sure they even know what they are looking at other than a mushroom cloud. I disagree with the expert quoted in the film who says that there is an appreciable difference in terms of size between the two (the Hiroshima and Nagasaki bombs were 15kt and 20kt respectively; that is not a significant difference from a damage point of view, or from the point of view of their clouds — any significant apparent differences in size are due to how far the plane is from them).

I know of no study on this that you can cite. It would be interesting to do a historical survey of depictions of the bombings in different media over time. I have noted in the past that only a few photographs and images are "re-used" many times over when it comes to depicting nuclear explosions, and the Internet has allowed even fake CGI mushroom clouds to masquerade as real ones. But these are just impressions, nothing systematic.

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