Any paint made with milk is milk paint.
Traditionally it is made with lime. Borax is another caustic alkali, like lime but more mild, that works as an emulsifier for the casein protein and water. Ash or ammonia also does this. Borax is a salt, and may crystalize over time, but is supposedly more durable than lime. Lime tends to make the paint more milky than borax. Ammonia carbonate is clearest but smells.
As I understand the casein powder processing, it comes from curdling milk with acids, and draining off the whey. Powdered milk is made by spray drying (whole or non-fat milk) and leaving condensed solids. Powdered milk may actually work for casein paint making, but may also contain additives I wouldn't need.