What is the difference between TID16/SID16 and TID7/SID7?

[kiasta]

I'm trying to port some code to the switch, starting with SWSH. I am able to get some basic trainer data, but I've noticed that in the PKHeX app the TID/SID are basically split up from the ID32, like so: TID7: XXXX------ SID7: ----XXXXXX of the ID32. While the "ID" is actually just TID16/SID16 and not ID32.

While debugging PKHeX we have these TID16/SID16 and ID32 values:

But in the app itself they are displayed as such:

I'm also getting the same values on the switch as the debugged values in PKHeX (before debugging PKHeX to see the raw values, I spent over an hour trying to figure out if I was using the correct offsets and the right key):

Here is where they are calculated:

private void LoadTID7(ITrainerID32 tr)
{
    public static uint GetTrainerTID7(this ITrainerID32 tr) => tr.ID32 % 1000000;
    public static uint GetTrainerSID7(this ITrainerID32 tr) => tr.ID32 / 1000000;
}

Then we have these properties that are setting these values, which I'm assuming means that they are simply a formula to generate a valid ID32 value:

public static uint SetTrainerTID7(this ITrainerID32 tr, uint value) => tr.ID32 = ((tr.ID32 / 1000000) * 1000000) + value;
public static uint SetTrainerSID7(this ITrainerID32 tr, uint value) => tr.ID32 = (value * 1000000) + (tr.ID32 % 1000000);

Am I wrong about this? Is this a formula that Pokemon uses to generate ID32 values, or is this just your own method? Sorry if this seems like a stupid question, I just want to make sure I properly understand what these values are for, instead of assuming.

EDIT: I updated the image to include my Shield cart so there's no assumption of piracy.

[Lusamine]

The same bytes for TIDSID are converted in 2 different ways. Those are methods used by the games, and PKHeX is showing the values the way you would see them in-game.

The method to get the 5 digit TID/SID is used for Pokémon from gen 3-6, and the method to get the 4 digit SID with 6 digit TID is used in gen 7 and after.

For example, let's say your TIDSID is the 4 bytes 46 85 3E 43 in the Pokémon data.
The SID16 is 0x433E = 17214.
The TID16 is 0x8546 = 34118.

The TID7 and SID7 would be obtained because 0x433E8546 = (1128)170822, which gives TID7 of 170822 and SID7 of 1128.

You can enter these values into PKHeX to verify.

[kiasta]

The method to get the 5 digit TID/SID is used for Pokémon from gen 3-6, and the method to get the 4 digit SID with 6 digit TID is used in gen 7 and after.

This was the part of the puzzle I was missing, I didn't realize these values were specifically for gen 3-6. I didn't even think about that! Thanks for the detailed explanation, it makes sense to me now!