Apologies for the delay in responding.
model.binvox files are surface voxelizations (i.e. voxels are produced only on the 3D mesh surface)
model.presolid.binvox files are solid voxelizations (i.e. voxels are filled in for the interior of the 3D mesh)
model_1.binvox files are intermediate result voxelizations that should be ignored.