Yeah, the list does seem to confuse less. And it is definitive.
The formula is: you can break your original FAP into any of the lower-down splits: that is, 1 War can be split into 2 Battle, 4 Raid, 8 Skirmish or 12 Patrol. You can then re-split one of those points (no more than one), into 2 of the level below. And re-split one of those, into 2 of the next level.
So you could not split 1 War into 2 Battle, and split them both into 4 Raid. And you could not split 1 War into 2 Battle, and split one of those Battle into 4 Skirmish. You could however simply split your 1 War directly into 4 Raid, and split one of those Raid into 2 Skirmish, and split one of those skirmish into 2 Patrol. So you'd end up with 3 Raid, 1 Skirmish and 2 Patrol.