flying in the same air, with the same wing area but with a different wing profile (just an example of an influencing factor) will have a different value of CL
You're explanation is lacking in why the CL would be different. If B has a different CL to A, but wing area and velocity are the same, that would mean that the one with the higher CL would be climbing relative to the other, or descending less slowly. If both A and B are in level flight the CL will be exactly the same, though the angle of attack will more than likely differ.