Correct, a mature rain forest stores carbon in a living system but adds or detracts little from the athmosphere. If destroyed, the carbon stored is released.

A dusty memory of an old figure says that about 25% of the carbon attition to the athmosphere is (was) the result of decreasing rainforest.

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When a tree is growing, carbon gets locked away, ergo, growing trees are net sinks. BUT there have been some pointers that growing trees also emit methane gas - which is an even stronger greenhouse gas. I don't know what the net effect is of these two processes.

After trees reach their optimum, while there is no net storage, trees remain a temporary reservoir for carbon for as long as they live. After death of a tree, the carbon is returned to the biosphere, and some of it to the atmosphere. As skod points out, burning tropical forests gets a lot more carbon in the atmosphere. And that's why increasing droughts in the tropics are also bad news.

However, human bodies are the same like trees - as long as we live, we are a temporary reservoir effectively keeping carbon out of the atmosphere.

Hence my proposal: a solution for reducing the greenhouse effect is to have more people on the planet! :)