Global cooling was a hypothesis of the looming cooling of the Earth's surface and atmosphere that would take place over a period of substantial glaciation.
It emerged as a result of a drop of temperature during the period of 1940s and 1970s. After this it was realized that it is not a big threat as global warming.
On the other hand, Global warming is the rise in overall temperature of the atmosphere which is caused by greenhouse effect that is as a result of rise in the levels of greenhouse gas emissions such as CFCs and carbon dioxide.
Global warming is a present threat in the society world over with the rise in temperatures and climatic changes taking place, this is the reason why global warming replaced global cooling.