In the context of climate change and in particular mitigation, a sink is defined as "Any process, activity or mechanism which removes a greenhouse gas, an aerosol or a precursor of a greenhouse gas from the atmosphere".
In the case of non- greenhouse gases, sinks need not store the gas. Instead they can break it down into substances that have a reduced effect on global warming. For example, nitrous oxide can be reduced to harmless N.
Related terms are "carbon pool, reservoir, sequestration, source and uptake". The same publication defines carbon pool as "a  reservoir in the Earth system where elements, such as carbon [...], reside in various chemical forms for a period of time."
Both carbon pools and carbon sinks are important concepts in understanding the carbon cycle, but they refer to slightly different things. A carbon pool can be thought of as the overarching term, and carbon sink is then a particular type of carbon pool: A carbon pool is all the places where carbon can be (for example the atmosphere, oceans, soil, plants, and fossil fuels). A carbon sink, on the other hand, is a type of carbon pool that has the capability to take up more carbon from the atmosphere than it releases.