One way to understand scoring is by imagining a theoretically completed board: one where the players filled dame (as usual with area scoring) and then prisoners are also filled back into territories of their color (as usual with territory scoring).
This board includes all stones ever played, and gives the same score as normal (since filling dame doesn’t affect the Japanese score, and backfilling prisoners doesn’t affect the Chinese score).
And now the relation between scoring systems is clear: since stones on the board are equal for both players (or B at most have one extra), you get the same result whether you add them to territories or not. Either way it’s determined by those territories (which already have the prisoners accounted this way).
I think this ultimate board also has beauty and teaching value: with all played stones staying on it, it shows that the only thing the players compete in is how well they have placed those stones.