Genetic modification (GM)of crop plants is frequently described by its proponents as a continuation of the ancient process of domestication. While domestication, crop breeding, and GM all modify the genomes and phenotypes of plants, GM fundamentally differs from domestication in terms of the biological and sociopolitical processes by which change occurs, and the subsequent impacts on agrobiodiversity and seed sovereignty. We review the history of domestication, crop breeding, and GM, and show that crop breeding and GM are continuous with each other in many important ways, but represent a momentous break from domestication because they move plant evolution off of farms and into centralized institutions. The social contexts in which these processes unfold dictate who holds rights to germplasm and agricultural knowledge, shape incentives to effect particular kinds of changes in our crops, and create or constrict biodiversity. Presenting GM as a continuation of domestication puts forward a false equivalency that fundamentally misrepresents how domestication, crop breeding, and GM occur. In doing so, this narrative diminishes public understanding of these important processes and obscures the effects of industrial agriculture on in situ biodiversity and the practice of farming. This misrepresentation is used in public-facing science communication by representatives of the biotechnology industry to silence meaningful debate on GM by convincing the public that it is the continuation of an age-old process that underlies all agricultural societies.