Mismatches are due to vBlank interrupts. vBlank will interrupt at inconsistent places depending on nature rolling and hardware/emulation used. Theoretically any Method 1/2/3/4 is possible. Stationeries are interesting because the likelihood of a non Method 1 on the actual GBA is near or exactly zero.
Edit: Also it is technically broken up into several sub categories too (first party pokemon ability not taken into account).
Method-1-1, Method-1-2, Method-2-1, Method-2-2, Method-3-2 (The 2 makes it Method 3), Method-4-2 (the 2 makes it Method 4)
Where the second number is the number of vBlank interrupts between battle start and end of IV generation. Generally the exotic ones only happen when fishing or in caves while playing on an actual cart.
IIRC, on some emulators Method-4-1 is possible due to bad timings.