The term was changed because "climate change" is a better descriptor for people to understand the issue.  A big part of this was to counter the denier tactic of spreading uncertainty with such comments as "so much for global warming, did you see how much snow we got last night".

"Global warming" appears to be happening, but it results in changes in weather patterns (either temporary or long term) that can see some parts of the world get cooler even while  the planet on a whole appears to be warming.  There is also the fact that big fluctuations naturally occur even when the long term trend is upwards (in temperature).  This is why next winter may be colder than the past one, but the average winters have been getting less severe over the years in many areas.