The core and global properties of the early-type ("red sequence") galaxies in the Virgo and Fornax clusters are examined using high-quality HST/ACS imaging for 143 galaxies. Rather than dividing neatly into disparate populations having distinct formation and/or evolution histories, many of the core and global properties of these galaxies show smooth and systematic variations along the galaxy luminosity function. The few examples of the rare class of compact elliptical galaxies in our sample all show properties that are strongly suggestive of tidal stripping by massive galaxies; if so, then these systems should not be viewed as populating the low-luminosity extension of so-called "normal" elliptical sequences. These results demonstrate that complete and/or unbiased samples are a pre-requisite for identifying the physical mechanisms that gave rise to the early-type galaxies we observe locally, and how these mechanisms varied with mass and environment.