The traditional glasses free 3d monitors rely on special coatings on the glass to "split" the direction of a pixel. Some coatings are electronically controlled (like Sony's), some are physical (lenticular filters) It still displays a 2D projection of a 3D image, but twice.

By contrast, my understanding is lightfield displays projects the entire volume. So you don't have a pixel, you have a voxel. So each eye gets a different bit of the same voxel