Both are small milk coffees in a little glass. A piccolo is a single ristretto topped with silky, slightly foamed milk, like a baby latte. A cortado is a double shot cut with an equal amount of warm milk and almost no foam, so it is stronger.
The differences
Shot: a single ristretto in a piccolo; a double espresso in a cortado.
Foam: a piccolo has a little silky foam; a cortado has almost none.
Origin: the piccolo is Australian; the cortado Spanish.