W/m-K (Watts per meter-kelvin) is a measure of thermal conductivity of a substance. This does not tell you the performance of a heatsink - only the performance of the material used to construct it (e.g. aluminium or copper). It is the only thermal property of a substance that has significant relevance to heatsink performance. Copper has a higher thermal conductivity than aluminium: of a Cu and an Al HS of identical volume, area and design, the Cu one will always outperform the AL one.
K/W (Kelvin per Watt) specifies the performance of a heatsink under given conditions (specified air flow and orientation). It is dependent not just on the HS design and materials but whether air flow is forced or restricted, and the velocity of airflow - it even depends on altitude (due to differences in air pressure). This value is very useful - e.g. a 1 K/W heatsink will rise 1 K (equivalent to 1 C) above ambient temperature for every 1 W of power it has to dissipate. This number is not easily calculated - it needs to be measured under the conditions you are interested in. Examination of the HS manufacturer's datasheet may give you the answer you need.
