Left is a picture of Birch bark, Tenderboiled Terrine, Marrow Dumplings and a Dead Silk Runner in a clay pot, ready to be boiled. The pot could also boil the mushrooms if needed.
Right is a picture of a failed attempt at putting these objects into a cauldron.
I'm not sure if this is intended, but the cauldron can not be used to boil anything but mushrooms. I tested Birch bark, Tenderboiled Terrine, Marrow Dumplings and a Dead Silk Runner. None of these could be put in the cauldron for boiling, but the mushrooms Witch Hat and a Waxing Toad Stool could.