These are two totally different kinds of paint.  Both have advantages and disadvantages and can be used in a variety of ways.  Here are some of the similarities and differences…
Milk Paint comes in powdered form and needs to be mixed with water.  Chalk-type paints are sold in a tradition liquid quart.
Milk Paint has great adhesion on raw wood that will never chip/peel or fade.  Add the bonding agent to milk paint for use on previously finished surfaces to improve adhesion.  A quick sand to scuff up the surface will also help the paint adhere.  Chalk-type paints have great adhesion on most any surface without the addition of a bonding agent.
Milk Paint will show wood grain in most cases and can be used as a stain.  Chalk-type paints are thicker and cover wood grain in most cases.
Milk Paint can be distressed and/or crackled and will resist some finishes giving an authentic chippy, aged look.  Chalk-type paints can be distressed and crackled, but will not chip.