I guess the first position of any chord is the open chord, which is obviously the D shape for the D chord, so the second position is C shape (based on the CAGED order).
Let's take another example. The first position of the G chord is the G shape (the open chord), so the second position is the E shape.
Therefore, the first or any position is not always the same. It depends on the chord itself.
I may be wrong tho.