Dairy products are generally defined as foodstuffs produced from milk. A production plant for such processing is called a dairy. Raw milk for processing generally comes from cows, but occasionally from other mammals such as goats, sheep, water buffalo, yaks or horses.
Grocery stores in North America (and beyond?) often stock eggs very near to "real" dairy products, such that one can often find cartons of eggs sitting under a sign saying "dairy". This could conceivably be either a cause or an effect (or both) of the conception of eggs as dairy products.