Typically when you see a pepakura pattern that's labeled as "Foam" there are two main differences from a standard pepakura paper template file. The first is what you already pointed out, the flaps are turned off. The second is that small bits which in building out of paper would create depth will be removed or moved outside of the pages area as you can use the thickness of the foam to create that depth instead of having to cut out and glue those pieces.
For example here you can see the inner chest piece for an ODST as the file is laid out for pepakura. You have the tabs and a bunch of tiny little pieces
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Whereas this is the same file but modified for foam with the tabs turned off and all of those little bits being moved outside to where they won't print as you'll be using foam thickness instead.
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Not represented by this example but sometimes also the case is you might have only half the model within the page region such that you would mirror the parts for the other half. Useful for foam as it saves you pages of printing and cutting when you can just flip the part over and trace it again for the mirrored side.