Climate pertains to the Earth’s Atmosphere, or The Sky so to speak.
“Climate Change” was previously known as “Global Warming”. A warming Atmosphere causes a low or falling barometric pressure. Barometric pressure is also known as Atmospheric Pressure. It could be said the Atmospheric Pressure is falling. Since this on a global basis, the correct terminology would be “The Sky is Falling.”
I hope that clears things up.
To say that air pressure and temperature changes is to say nothing.