Sometimes the terms ‘global warming’ and ‘climate change’ are used interchangeably in everyday conversation. I don’t think there is too much of a difference if one is talking generally about the human-caused increase in global average temperature and its associated impacts. Nevertheless, they do describe different things.
Global warming. It’s a warming that has to be global. Obviously. It doesn’t have to be a year-on-year increase in temperature. We have no more reason to expect every year to be hotter than the last than we do to expect every month, or every day to be hotter than the last. There are other causes of variation in temperature. The rising and setting of the sun, the changing of the seasons, the switching of the tropical Pacific from a heat-absorbing La Nina to a heat-giving El Nino, and so on. But the central point here is that it strictly describes just the temperature of the Earth.
Climate change. This is a little harder to define. ‘Climate‘ is the average conditions in the atmosphere (‘what we expect’). It is not limited to temperature. Sure, temperature is important, but so is rainfall. So is the wind. ‘Climate change’ encompasses all these. The climate is never entirely stationary. It can change subtly over time or it can undergo wild swings such as those the Earth saw during its Ice Ages. No climate scientist claims that climate change can only be caused by humans.
I think ‘global warming’ is a better term to use unless one needs to explicitly include non-temperature effects on climate. Granted, it does imply (incorrectly) that it includes year-on-year warming. But it also encapsulates the problem more concisely than ‘climate change’, which can feel like a vague buzzword. As I have explained, it’s not vague, it just includes things other than temperature effects. It’s useful because some of the most significant impacts of increasing atmospheric carbon dioxide levels might not be temperature effects. They might be related to droughts, storms, sea-level rise, ocean acidification, and so on.
The term ‘climate change’ certainly has its place if you genuinely need to go beyond temperature and include all the impacts of increasing atmospheric carbon dioxide. If you are talking specifically about sea-level rise, talk about ‘sea-level rise associated with global warming’, not generically about ‘climate change’. That’s because the single best way to get people to understand what you’re talking about is to, you know, tell them what you’re talking about.
EDIT: NASA disagrees with my preference.