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The difference is that coal contains carbon that has been locked inside the earth's surface for at least a few million years (if not longer).

Trees on the other hand contain carbon that those trees extracted from atmospheric CO2 while growing. Burning those trees merely returns CO2 to the atmosphere that was taken from it a few decades ago. If you do that in a balanced way (growing the same amount of trees that you burn at any point of time), you may create a cycle that does not affect long-term atmospheric CO2 concentration.