A snazzy martini glass can even replace the cone. Think daiquiris, mojitos and piña coladas and tinker accordingly. Frozen concentrates made for blender drinks can do double-duty as snow cone syrup.

The difference between the variations of icy treats is more than the names, writes Nadia Roden in “Granita Magic,” a guide for home cooks. For snow cones, syrup is poured over crushed ice. For ...