An animal product is any material derived from the body of an animal. Examples are fat, flesh, blood, milk, eggs, and lesser known products, such as isinglass and rennet.
Animal by-products, as defined by the USDA, are products harvested or manufactured from livestock OTHER than muscle meat <https://www.ers.usda.gov/topics/animal-products/animal-production-marketing-issues/glossary/>. In the EU, animal by-products (ABPs) are defined somewhat more broadly, as materials from animals that people do not consume <https://ec.europa.eu/food/safety/animal-by-products_en>. Thus, chicken eggs for human consumption are considered by-products in the US but not France; whereas eggs destined for animal feed are classified as animal by-products in both countries. This does not in itself reflect on the condition, safety, or "wholesomeness" of the product.
Animal by-products are carcasses and parts of carcasses from slaughterhouses, animal shelters, zoos and veterinarians, and products of animal origin not intended for human consumption, including catering waste (all waste food from restaurants, catering facilities, central kitchens, slaughterhouses and household kitchens). These products may go through a process known as "rendering" to be made into human and non-human foodstuffs, fats, and other material that can be sold to make commercial products such as cosmetics, paint, cleaners, polishes, glue, soap and ink. The sale of animal by-products allows the meat industry to compete economically with industries selling sources of vegetable protein.
Generally, products made from fossilized or decomposed animals, such as petroleum formed from the ancient remains of marine animals, are not considered animal products. Crops grown in soil fertilized with animal remains are rarely characterized as animal products.
Several diets prohibit the inclusion of some animal products, including vegetarian, kosher, and halaal. Other diets, such as veganism and the raw vegan diet, exclude any material of animal origin.