More simply put, what is the difference between freezing and precipitation when considering a mixture?
Take two scenarios:
First a mineral in water. If the temperature of this solution is lowered, the solubility of the mineral will decrease and eventually precipitate out of solution. This could be done in a cascade type setup so that each time, the solution is cooled further and the liquid phase becomes more and more concentrated in water.
Second, consider a mixture of ethanol and water. Here too, I could lower the temperature until crystals first form. They would be almost pure water, leaving behind a solution higher in concentration in alcohol. I could repeat this procedure until I reach the eutectic mixture.
In both cases, a drop in temperature is allowing a solid phase to form out of an aqueous solution, yet one is referred to as partial crystallization and the other is referred to as partial freezing. I am not sure I see the difference.