Crows and eagles move together.

A, taking the ground as a reference, the position of the crow relative to the ground has changed, so the crow moves relative to the ground; So, A is wrong;

BCD, the crow is resting on the back of the eagle. Crow and eagle are relatively static, so taking crow as reference, eagle is static; Taking the eagle as the reference, the crow is still, so BD is wrong and C is right.

So choose C.