The first is cellular respiration of plants that uses previously stored energy (visualized in this chart).

The second is when heterotrophs consume organic carbon below ground and respire carbon dioxide.

The sum of these is called soil respiration, which I think was the process you were asking about.

Even in wild environments, leaching eventually reduces the soluble nutrients and reduces total biomass (see Vitousek & Reiners, 1975, and a lot of Vitousek's later work). The leaching takes long enough that it's also an adequate shorthand to say that undisturbed soils will accumulate soil carbon.