What is the difference between a carbon sink and a carbon reservoir?
The difference is that a carbon sink accumulates carbon, whereas a carbon reservoir has accumulated carbon.

That is to say:

A carbon sink is an ongoing process which is increasing the amount of carbon stored in it.

Whereas although a carbon reservoir might exchange individual carbon-based molecules with other parts of the carbon cycle, as much will go out as goes in, keeping the amount of carbon in the reservoir broadly constant.

Both of these contrast with things such as coal seams and natural gas &amp; crude oil reservoirs that humans have tapped as sources of fuel; and leakages of methane from the ground: these were carbon reservoirs until the amount of carbon in them began depleting (e.g. through mining, well-drilling, or - in the case of methane clathrate leakages - ice melt), at which point they became carbon sources.