Here's what everyone gets wrong about plants: we used to think anything that grew out of the dirt and didn't run away was a plant. If it had a stiff box around its cells—a cell wall—scientists just slapped a 'Plant' label on it.
But that's like classifying a medieval knight and an armadillo as the same animal just because they both wear armor! Nature is way more subtle than that. We eventually looked closer and realized fungi are building their cell walls out of chitin—the exact same stuff in a beetle's shell. And those 'blue-green algae'? They're actually cyanobacteria playing a completely different game of cellular chemistry, without even a real nucleus. Just having a wall isn't enough; you have to look at how the wall is built and what's happening inside the house.
If you were a biological detective trying to sort these out, what kind of chemical clues would you look for to prove a mushroom and a fern don't belong in the same kingdom?