You are correct in saying that Fungi are not the same as plants

Both the plant and fungus kingdoms have some common characteristics. ... - - While both are eukaryotic and don't move, plants are autotrophic - making their own energy - and have cell walls made of cellulose, but fungi are heterotrophic - taking in food for energy - and have cell walls made of chitin.- -

I guess that I was just thinking that some animals can cross breed, and plants can cross breed, so why cant mushrooms cross breed? ;)