Assessing distances between images and image datasets is a fundamental task in vision-based research. It is a challenging open problem in the literature and despite the criticism it receives, the most ubiquitous method remains the Fréchet Inception Distance. The Inception network is trained on a specific labeled dataset, ImageNet, which has caused the core of its criticism in the most recent research. Improvements were shown by moving to self-supervision learning over ImageNet, leaving the training data domain as an open question. We make that last leap and provide the first analysis on domain-specific feature training and its effects on feature distance, on the widely-researched facial image domain. We provide our findings and insights on this domain specialization for Fréchet distance and image neighborhoods, supported by extensive experiments and in-depth user studies.