AAFCO defines “byproducts”, or “by-products” as “secondary products produced in addition to the principal product.” In the case of pet food, byproducts are typically “the excess material left over after processing human foods.”
The USDA separates animal byproducts into three categories: hides, inedible offal, and edible offal, with variety meats being a subcategory of the latter. In addition to skeletal muscle, or what you typically order at the butcher for yourself, certain parts of animals are considered edible when certain conditions are met. Beef liver and tongue are two examples.
The inedible offal, or byproducts, remain and “include hide or skin, hair, horns, teeth, fats, bone, ligaments and cartilage, feet, glands, blood, and lungs” (emphasis added), as well as the otherwise edible offal that has been deemed inedible, and they may be used in pet food if they are either canned or rendered. In Hill’s Science Diet Adult Light with Liver, a canned dog food, for instance, the third ingredient after water and corn, is “pork by-products”. These can include any of the items just mentioned. Moreover, save of “pork liver”, these “pork-by products” are the only meat in this dog food.
If not canned, however, the inedible animal byproducts can still be used to make pet food if they are rendered. Processors render byproduct meal by overcooking it and skimming off the fat. Sometimes the constituent animal of the byproduct meal is identified, as in “chicken by-product meal”, “turkey by-product meal”, “beef by-product meal” and “poultry by-product meal.” (Chicken by-product meal is further subdivided into two categories: feed grade and pet food grade.) Other times this byproduct meal is identified generically, with names such as: “meat meal”, “meat and bone meal”, “meat by-product meal” and “animal by-product meal”. This byproduct meal lawfully includes, but is not limited to, road-kill, dead zoo animals, euthanized house pets and diseased livestock.
Alpo Prime Cuts Dry Dog Food, for example, contains, after corn, “meat and bone meal”, which according to AAFCO is a “rendered product from mammal tissues, including bone, exclusive of any added blood, hair, hoof, hide trimmings, manure, stomach and rumen contents.” Neither a specific animal nor its condition is mentioned. In short, there is no way in knowing with any degree of specificity what this ingredient is. It could be filet mignon, or a euthanized pet.
 United States Department of Agriculture LDP-M-209-01; November 2011, Where the (Not) Meat? Byproducts from Beef and Pork Production. (Link).
 AAFCO, 2016 Edition, or http://www.aafco.org/Consumers/What-is-in-Pet-Food