Is the Reynolds number the same for both the airfoil and wing? If not, why/how does it change?
From the equation that defines it, you can see that its value depends on some properties of the fluid (air), the speed that an object moves through the fluid, and the length of the object.  Nothing else.

For an airplane wing, the length, aka "characteristic linear dimension," is conventionally chosen to be the chord of the wing.  The wingspan doesn't affect the Reynolds number.  Neither does the choice of airfoil.

In other words, given an airfoil (say, a segment in a wind tunnel at a particular chord, airspeed, and air density), and given a wing on an airplane built from the same airfoil with a different chord, airspeed, and air density, the Reynolds numbers for these two situations are likely to be different.