As per the title, I want to understand if the roll rate/pitch rate/yaw rate are same as the data obtained from mpu9250 gyro sensor along y-axis, x-axis and z-axis?
If not then how to calculate roll rate/pitch rate/yaw rate from MPU9250.
The RC Rates are just the multiplicator value the Aircraft will try to execute your inputs. The resulting speed (degrees/sec) are just estimates based on a typical hardware configuration, without a major effort, as this is very much dependent on the conditions the aircraft is in, the way the execution is carried out, and the hardware that actually does it.
As an example, an RC rate resulting in 500degrees/sec a 5" quad with 4 motors will be significantly faster than a 500degree/sec setting on a 10" quad or on an aircraft that uses mechanical elements to execute directional changes.
As another example: with a high Super rate resulting in the same mathematical 500degrees/sec a larger Quad will turn faster because of the momentum it creates, so timing is an issue as well.
That's why you set the RC/Super/Expo rate multiplier instead of the rate itself.
If the axes of the gyro sensor are aligned with the aircraft principal axes, then yes, the gyro data will correspond to the roll/pitch/yaw rates, of course after transforming the gyro value range to degrees. And of course like all sensor data the measurement contains noise and probably a, hopefully small, bias. If the axes are not oriented correctly, the measured values of the gyro axes must be transformed into to aircraft coordinate system.