There are several possible things happening here.
Most image display programs that can display RAW files but not intended to process them display the built-in JPEG preview. The camera creates this with the help of its internal JPEG engine and stores it with other data in the RAW file.
This shows a lot less effort and generally more useful than to display a default rendering of the raw file. (Do not forget that a RAW file does not have a valid interpretation.) See What does an untreated RAW file look like?).
But, if it is not that, consider also:
the Processing This is not the only thing that is different. The sensor itself is, as is the filter stack on the sensor (including the color filter matrix). And you Probably did not use the same goal. Even similar lenses transmit light slightly differently.
And if you take exactly the same image at the same time, the cameras are not in the same place; or, if they were in the same place, the pictures are not taken at the same time. This could be particularly serious if you are shooting under fluorescent lamps (including LEDs) and use a fast shutter speed.
One could use the algorithm of your RAW converter, which could produce different results just because of the differences above. But it is also possible that the RAW converter uses the "as shot" white balance, read from metadata in the image (and identical to the JPEG rendering of the camera).