7 1/4 to 8 3/4 brake swap

I'll be swapping my small rear with 9" brakes to an 8 3/4 with 9 " brakes. The small rear has all new brake parts. Will these easily swap onto the larger rear or are the brakes different? Wasn't sure if 9" was 9" regardless of rear size
I don't claim to have this all figured out but I think your backing plate and drum need to match your axle bearing to flange (where the wheel bolts up) offset. I think the offset is narrower on the small bolt pattern(4") and wider on the big bolt pattern (4.5"). You can buy aftermarket big bolt pattern (4.5") axles with with the narrow offset so you will need to measure. Hope this helps and if this is incorrect someone please correct it.