Artist grade paint is the more expensive of the two because it's made from ingredients of a much higher quality. You'll notice how artist paints are split into different series depending on what raw materials have been used to create it. The higher the series letter or number, the more expensive it will be.
You'll find that artist grade paint is the better grade of paint for coverage. In other words, you should easily be able to paint one colour over another colour without any problems arising.Mixing mediums into your paint allows you to be more experimental. You can give the paint extra properties, try out different techniques and make it match your needs better. You can add mediums to both grades of paint, but as you'd expect artist mediums are generally a bit more expensive than student ones.