Using images from the SDSS DR13 library, we examine the structural properties of 374 bright (classed E0 to E6) and dwarf ellipticals [classed dE(nN) to dE(N)]. The sample combines a multicolour sample of bright ellipticals (252 galaxies with $M_{\text{g}} < -20$) with a new sample of faint ellipticals (60 galaxies with $M_{\text{g}} > -20$) which overlaps the dwarf elliptical sample (62 galaxies) in luminosity and size. The faint ellipticals extend the linear structural correlations found for bright ellipticals into parameter space not occupied by dwarf ellipticals indicating a dichotomy exists between the two types. In particular, many faint ellipticals have significantly higher effective surface brightnesses compared to dwarf ellipticals which eliminates any connection at a set stellar mass. Template analysis of the three subsets of ellipticals demonstrates that the bright and faint ellipticals follow the same trends of profile shape (weak homology), but that dwarf ellipticals form a separate and distinct structural class with lower central surface brightnesses and extended isophotal radii.