Clear cutting refers to the cutting of trees, specifically all of the trees in one select area. Replanting is not done and this leads to deforestation.
Controlled burns have a completely different affect. They burn the under brush to help keep the soil rich with nutrients, plus they also help to prevent large crown fires that burn down whole forests from happening.
Clear cutting is a bad thing and controlled burns are a good limiter for a forest.
In fact, there is a Oceanic Carbon cycle! Carbon dioxide get absorbed by the ocean's surface from the atmosphere and then get converted into a dissolved inorganic compound and so on.