Animal by-products, as defined by the USDA, are products harvested or manufactured from livestock other than muscle meat.[3] In the EU, animal by-products (ABPs) are defined somewhat more broadly, as materials from animals that people do not consume.[4] 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
If I were to categorize in products and by-product intuitively I'd think meat was product and dairy and eggs by-products. Scince "CoWs GiVe MiLk AnYwAyS".