A "double foul" (and a "simultaneous foul") happen at (approximately) the same time. They "offset". The rest is just semantics.
My advice is to forget the "false double foul" category. It's just two separate fouls. They happen often, and are adminisstered correctly (as two separate fouls, each carrying their own penalty). No need to try to categorize them.
While the above might not be 100%, it will get you through almost all situations and form the understanding you need for any weird exceptions that are talked about ad infinitum on these boards.
One other thing -- it's dashes for rules (4-19-9) and dots for cases (4.19.9A)
