Good on you for even knowing about this obscure controversy. Of course I know the difference between various groups of Fungi. Some may resemble each other but are as different as jellyfish and corals and non fungi like lichen are amazing communities and not a single life form.
I once found a new species of a bright yellow mushroom and submitted its spores to the depository of life forms which is only 3 miles away. Unforunately they also store virus. The facilities has many incinerators and is quite an impressive place hiding in plain sight. I've noticed they get enourmous deliveries of liquid oxygen.