SLUSHY is a generic term for semi-frozen beverages. This includes, but is not limited to, Slurpee, Icee, Slush Puppies, or the frozen "cappucino" at 7-11.
Slushy is usually modified by either a color or a flavor, often interchangable. There is usually only one of any given color available at a time, and most slushies of the same color taste similar, so it is generally sufficient to say "I would like the red slushy", or similar.