An Icee or "frozen coke" is usually a carbonated beverage that is frozen while being tumbled in a freezer. Think of an ice cream maker you may use at home. The paddles in the freezer keep the liquid from freezing solid. These drinks normally expand when they leave the machine and go into the cup. Icees can normally be found at Target snack bars, BTW.
Anyway... I enjoy both types of frozen treat, and both will cause excessive "brain freeze." Enjoy!