In relation to the carbon cycle, if the trees were all cut, there would be an inversion in the cycle, directly affecting the absorption of CO2 by the plants. As a result, terrestrial global warming would increase due to the high rate of CO2 release into the atmosphere.
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.
