I kind of agree with the larger point about story telling vs evidence, but this cuts both ways. Your specific example about global warming vs climate change has a history in the US, but in the other direction (excerpt from internal Republican strategy memo):
> “Climate change” is less frightening than “global warming.” As one focus group participant noted, climate change sounds like “you’re going from Pittsburgh to Fort Lauderdale.” While global warming has catastrophic connotations attached to it [1]
> The phrase "global warming" appeared frequently in President Bush's speeches in 2001, but decreased to almost nothing during 2002, when the memo was produced. [2]
Reading the memo, he also goes on to suggest that the scientific consensus is closing against them, but the public is still uncertain, so there’s a window of opportunity for the party to spread doubt about this, and finding and promoting counter-experts works best.
I think, at the time, all these strategies were effective.
To be fair to (the strategist) Frank Luntz, he later had a change of heart, and now does the same stuff for policies on the other side of the issue.
[1] https://www.sourcewatch.org/images/4/45/LuntzResearch.Memo.p...
[2] https://www.theguardian.com/environment/2003/mar/04/usnews.c...