Powdered sugar better than using granulated sugar when making icing?!

Hm! That's really odd--maybe she was making more of a glaze?
But yeah, powdered sugar dissolves more easily and creates a creamier icing. So you shouldn't use granulated.
The difference between frosting and icing?
-Frosting usually has some sort of fat in it that makes it richer and creamier than icing. It's usually spread on cakes, as opposed to piping.
-Icing is generally harder and more sugary than frosting, as well as thinner and more liquid-y. It's generally used for piping, as opposed to spreading.

So your birthday cake is covered in white frosting, but the "Happy Birthday" message, as well as the pink squiggles on the side, are icing.

You can't make buttercream with granulated sugar. Maybe she was making something else, like a glaze, that's cooked? Or divinity frosting?

Those words are pretty much interchangeable in the regular cook's mind, though I remember icing as a cooked sweet covering, while frosting is uncooked.

yes because it makes a thicker icing without having any clumps of sugar

years of cooking

powdered sugar is better. makes the texture moore creamier