I do know how hydroponics works. I think aeroponics is just like cloning but in a big scale you just have to use big buckets and keep air and water at all times with chemicals .
Hydroponics is specifically using water (without soil) to grow plants. Aeroponics is using air+water (mists, micromisters), no soil, and the roots are usually suspended in the mist.
Aeroponics is useful on rooting because the right amount of oxygen and water are available to the roots compared to the sometimes partially anaerobic conditions in traditional hydroponics.