It appears that I was trying to correct a misconception you do not actually hold. I've seen apparently well meaning people claim that "global warming" was rebranded "climate change" by Frank Luntz to make it sound less scary, while both terms have been in widespread use among scientists since before the issue became widely known among the public.

Yes, but more to the point, they are not synonymous except in very recent history. Theories of climate change were needed to explain evidence of the Ice Age long before anyone thought that warming was a concern, back in the early 19th Century. The evidence that climate could change was also generally distinct from the evidence which established that CO2 could change the climate. Global warming is a subset or result of climate change.