That's an euphemism ;-) considering a huge 800/2 difference between two top RAW converters. As if they describe two completely different things.
Not quite. They describe the same thing, but because of using different assumptions of the actual color the resulting numbers differ. Yet that doesn't prevent them from Click white balancing correctly, because that now starts from the same assumptions (color coordinates in a defined trichromatic color space). The solution depends on the assumption of an XYZ color from the Raw image data, and the outcome depends on which color is actually used. Use the same assumption, you'll get the same output from the algorithm.
The main thing is that the color temperature and tint values should not be taken as absolute numbers, but rather as an approximation, and relative differences within that application will suggest the magnitude of the visual difference. Comparing or transferring color temperature numbers between different applications is not something I would recommend doing.
Here's some more background on the determination of the CCT:http://en.wikipedia.org/wiki/Planckian_locus#Correlated_color_temperature