Leather as you know it are combinations a few different (known) structural proteins secreted from mammals between skin cells, after the skin cells themselves have been removed, and the proteins become chemically glued together (cross-linked). The majority of that protein is collagen.
Plether is a plastic fiber (petroleum derivative) that is spun and processed in such a way as to have an appearance similar to the final leather product (kind of, close enough). It's not protein-based in any way.
This new leather, 'Mylo', is a protein-based 'fabric' where the base protein is secreted by fungi rather than mammals. However, fungi are similar enough to mammals evolutionarily, that the proteins they secrete are evolutionary related to those secreted by our own cells to make our skin. The primary protein in both cases is collagen. Additionally, fungi genetics are easily manipulable, so you can actually insert the DNA that encodes for mammal-like collagen, other proteins found in animal leather, or proteins with new or completely different functions that would never show up on the skin of a mammal (color, water resistance, enzymatic capabilities, etc.).
tldr: Pleather is nothing like animal leather chemically - but has some similar bulk properties. This new MyLo is chemically related (evolutionarily) to animal leather, but ultimately comes from fungi. But because it's genetically known, it can actually include new capabilities that cannot be found in animal leather.