Aeroponics is a subset of hydroponics but has some important distinctions. While both methods refer to growing plants without soil, hydroponics involves periodically immersing in or covering plants' roots in water. Nutrient film technique, ebb and flow, drip, and deep water cultivation all share that practice.
Aeroponics focuses on providing plenty of air to the roots, so it never immerses or even substantially covers the roots with nutrient solution. Periodic misting punctuates relatively longer periods resting in a high-humidity environment where plants can efficiently absorb and use both water and nutrients. Lack of oxygen produces problems like poor growth and root rot, and hydroponics systems attempt to correct for that by adding aeration to the nutrient solution, but with aeroponics, the solution is built into the system.