That's... not true at all. The increasing use of the word 'climate change' as opposed to 'global warming' is because global warming refers only to the general trend of warming while climate change is holistic, and includes other climactic trends due to greenhouse emissions, like the increased intensity or frequency of storms and disruptions in weather patterns.
It has nothing to do with partisanship, 'political correctness', or whatever else and everything to do with the fact that scientists like to use terms that are accurate and precise, and will update their vocabulary to reflect our most accurate and precise understanding of the issue.
Global warming is a perfectly fine phrase to use, so is climate change. They have similar meanings, but one is solely about a singular symptom (global warming), and the other reflects the situation as a whole (climate change).