Equivalent Cyclohexane Structures?
Yes, the two structures you've drawn are the same; both substituents are in axial positions.  The two structures shown in the link you provided are not the same; they are conformational isomers.  The one on the left is the same as the one you've drawn with both substituents in the axial position.  The one on the right has both substituents in the equatorial position.  These two conformational isomers exist in equilibrium with the (e,e) isomer favored.  The two conformers interconvert by a cyclohexane ring flip.