Secondary SDCard question

I was under the impression that all alternative OSes used the same conventions/folder structures for SDCards so that you could just swap the OS sdcard and keep the ROM sdcard intact. So I spent hours transferring files to my ROM sdcard (stock OS) and then decided to migrate to Knulli. To my surprise it does not accept my ROM sdcard.

I have the ROM sdcard as a FAT32, and I suspect that might be part of the issue. But apparently the folder structure is also very different and - I'm assuming - incompatible.

Is my understanding correct here (that each OS needs their own SDcard structure, making it impossible to just swap the OS card and keep the ROM card)? Or am I missing some setup to make this process easier?