A Cortado comes from the Basque region of Spain and is made with equal parts milk and espresso — hence its name, "cortado," the Spanish word for "cut."
While it does also bring the drink a hint of creaminess, the cortado is unique compared to other coffee drinks in that the milk is only lightly steamed without any froth or foam.
The piccolo is a drink that champions the taste of the beans. It accentuates the espresso itself, using only just enough milk for all of its flavor to shine and no more.
The piccolo is unique because it uses 1 part espresso to 2 parts steamed milk, specifically pouring what's known as a single ristretto espresso most often served in a small glass.
Both drinks are made with different ratios of milk to espresso, with the piccolo containing ⅔ milk compared to the cortado's ½. They also have different types of espresso shots.
The cortado's espresso is significantly less "cut" through, partly due to the standard espresso shot having more of a bitter and intense coffee flavor in the first place.