Smoothie - water as base liquid, originally?
Generally people don't use water, because they don't want watered-down flavors. Fruit juice, milk, and yogurt all provide some flavor, so people tend to like them more.

But you certainly can use water if you want. It'll probably work best if you have some good flavorful fruit, and you might end up wanting to add extra sweetness, but it's possible. (I personally don't mind using ice, to get it extra cold with more icy texture, but that's not universal.)

In any case, it's not a strictly defined term; if you have a frozen drink that tastes like it's made out of actual blended fruit (and dairy and whatever else), I'm sure people will call it a smoothie.