How large an energy difference in Hartree can be used to distinguish two different structures? For example, I use two different geometries of the same molecule to do optimisation in Gaussian, and the two resultant geometries look roughly the same. The energy difference between the two optimised geometries is only 0.0000001 a.u.. So can I view them as the same geometry? Or is the energy difference large enough to distinguish them? How large an energy difference is large enough for you to see two geometries as different geometries?
I wouldn't use energy as a general criteria to discriminate conformations; a root mean squared deviation (RMSD) of superimposed structures would be a better metric. This is because two very different conformations may have very similar energy. For example, if you perform a relaxed energy scan of one of the dihedrals of cyclopentane, you get nearly the same energy for most of the dihedral angles, bu very different ring conformations.

If you found an energy difference of 0.0000001 a.u. and the superimposition of the conformations is nearly perfect, I'd say they are in the same minimum of the energy surface.