In case of global temperatures we are interested in aggregate values rather than local distributions. Is this the reason we can accurately predict one but not the other?
Correct. Think about sitting by a little stream and looking at how it flows around a rock. There will be eddies that go this way and that way, and they are pretty chaotic. So you can't accurately predict the exact velocity of the stream at one place for a time that is more than two or three times as large as it takes for an eddy to move past that time. That's the equivalent of the weather.
But you can accurately predict the average velocity at the point long in the future -- it will simply be the current average velocity plus or minus a correction you can compute if you know whether the volume of water the stream transports per second increases or decreases between now and the point where you need your correction. That's the equivalent of climate.