Romantic Tutu: is a  three quarter length A-line or bell shape skirt with 1 or more layers of tulle, and sometimes chiffon. It was either invented by or  popularized, by Marie Taglioni

A Powder Puff Tutu is short, made with tulle and has a puffy- full look. It was named for Balanchine/Karinska Tutu

A Classical Tutu - aka Pancake tutu is tulle that sticks straight out in a perfect circle. It is made with a hoop, and layers of net

Classical Tutu (bell): It is a very short and stiff skirt made from layers of netting with a slight bell shape and fitted bodice. It extends outwards from the hips and does not use a wired hoop. It is usually longer than a classical (pancake) tutu. These can be seen in the famous ballet paintings by Degas