They are both made from dried grapes.
However, Amarone is a dry wine while Recioto is a sweet wine.
Both wines must be made from 40-80% Corvina grapes and need to be raisined in special drying lofts or drying rooms (aka appassimento) for several months after they have been picked.
Amarone is a rich, dry wine normally reaching alcohol levels of 15%. Once the grapes have been dried, they are crushed and fermented to dryness (but not before 1 December following the harvest). The fermentation takes a long time as the grapes lose around half of their liquid while they are being dried and are very rich in sugar. The wine is then aged in cask or, increasingly, barrique. The legal minimum alcohol for Amarone is 14% but the majority reach 15% and higher. They can taste like vintage Port but drier and without any fortification.
Recioto della Valpolicella cannot be crushed until 1 January and is then fermented. It is a sweet, unfortified wine with lots of fresh black fruit and cholocate. It usually reached an alcohol level of 12% with a high residual sugar of 250 grams/litre).