Airplane B, 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
Beg to differ. Given the attributes you describe, same wing area different airfoil, the Cl will be the same, as the formula shows.
L=0.5*A*ρ*CL*V^2
where:
L = Lift force
A = Surface Area
V = Velocity of air
ρ= Density of Air
CL = Coefficient of Lift
Given a different airfoil the necessary Cl will likely be achieved at a different angle of attack, dependent on the lift slope of the airfoil used.