My understanding is that millboard is a better quality board then greyboard. The finish is slightly smoother. The thickness is more carefully regulated. The strength is greater ~ as is the cost.
The manufacturing mill achieves this by using better quality ingredients. The recipe will still include recycled fibres but a higher proportion of longer fibres ~ probably a greater quantity of virgin fibre. The adhesive added to the mix is likely to be of better quality ~ probably more resinous ~ than for greyboard.
Some manufacturers produce extremely good quality millboard. So thick and strong that is it difficult to cut ~ beware!