In this paper we perform an in-depth description of the main properties and families of the introduced ordered weighted logarithmic averaging distance (OWLAD) operator, the generalized ordered weighted averaging distance (GWLAD) operator, and the generalized ordered weighted logarithmic averaging distance (GOWLAD) operator. These operators have as foundation the well-known Hamming distance measure and the generalized ordered weighted logarithmic averaging (GOWLA) operator. Furthermore, we analyze multiple classical measures to characterize the operators' weighting vectors and we present alternative formulations of the operators based on the ordering of the arguments.