Population Dynamics in Purebred Dogs

Anyone in the dog world has heard terminology thrown around about breeding, genetics, and the way breeding decisions affect breed populations as a whole. Coefficient of inbreeding (COI), line breeding, outcrossing, purebreds, mixed breeds, mutts, genetic diversity, health testing, color genetics, and heritable diseases are all hot topics, but what do these terms really mean? Do people in the dog world understand how to accurately use these terms? How has the dog world co-opted terms and misunderstood the scientific concepts behind genetics? Do we really understand how genes work within a population?