Dogs are sometimes referred to as omnivores, because they have the ability to survive on a diet which includes plant material. This ability does not make them omnivores - any more than the ability of intensively farmed cattle to survive on a diet that includes ground up animal components changes them from being herbivores to omnivores. We know that dogs are able to digest some level of starches / carbohydrates - but it does not follow that including these in the diet will benefit health - especially in the common forms included in processed diets. If we look at the anatomy and physiology of dogs - they are carnivorous. Some ecologists refer to them as 'scavenging' or 'opportunist' carnivores: these are carnivores which will eat wild prey when it is abundant and safe to do so, but will survive on whatever else it can scavenge (such as plant matter), when prey is scarce. Some refer to dogs as hypercarnivores.
Cats are usually referred to as 'true' carnivores. They have an absolute requirement for the amino acids present in a diet of prey. Cats are able to balance their own diet by hunting wild prey. Many domestic cats lack the opportunity to do this, or are disincentivised by the constant provision of processed foods.
"When unsuccessful {at hunting}, cats fed commercial foods will be held in a chronic state of nutritional imbalance. This raises welfare concerns, and will also in the long term likely affect cat metabolism and health (Martin et al. 2010)."
Quote from: 'The Nature of Nutrition: A Unifying Framework from Animal Adaptation to Human Obesity', by Stephen J. Simpson & David Raubenheimer