When I craft a paperbark sapling and plant it, I get a tree with paperbark wood on the exposed trunk, but jungle wood beneath the leaves. When I use an axe on the paperbark, the wood does not drop, although the jungle wood does.

In order to move fruit blocks (this includes paperbark, maple syrup, and cinnamon logs) you need to use shears.

I'll look into making the paperbark trunks more uniform.