TL;DR Let's keep climate-change as the primary and make global-warming a synonym.
There is definitely a difference between global warming and climate change (scroll down) but of course the question is whether that difference is useful on this site. Consider the first line from our on-topic FAQ:
Sustainable Living Stack Exchange is for people passionate about living lives in a sustainable manner ...
Although it's true that both global warming and climate change are on-topic here, they're only on-topic when the question is about the active practice of living sustainability. The actions we take and the way we choose to live may have some impact on global warming and climate change, but not selectively one or the other. So even though there is an academic difference, I agree that they can be considered equivalent and interchangeable in the context of Sustainable Living.
Although they describe slightly different phenomena, that level of nuance isn't particularly useful on this site. Earth Science Beta had a similar discussion, and agreed to use climate-change partly because it was internationally adopted by the IPCC in the 1980's.
Furthermore, I would expect that most questions intending to use either of these tags should first strive to use tags that show how the subject is connected to global warming, such as carbon-footprint or greenhouse-gas-emissions. (See the related meta discussion about which of those tags to use.)
Global Warming vs. Climate Change
Global warming describes the gradual increase of heat energy trapped in the atmosphere, crust, and predominantly in the oceans. Measurement is well understood, and short-term predictions (~5 years) are fairly easy to make.
Climate change describes the different ways that an increase of heat energy becomes visible, and the way it changes our lived experience. The lens of climate change also recognizes that heating effects are not uniformly distributed; while some regions may notice an increase in temperature, others might observe a temporary decrease, or changing wind patterns, or increased precipitation, or a difference in animal migrations.