Would it be correct if we say that rain is done in the upper troposphere while dew done in the lower troposphere? Or there are better definitions for the main difference between them?
Rain is formed by Collision-Coalescence or the Bergeron-Findelsen process. The cloud droplets are formed by the condensation of water vapor on aerosols, when the air reaches supersaturation via the Kelvin Effect and Raoult Effect (which makes up Kohler Theory).
Hope this helps.
However, hygroscopic nuclei play an important role in case of rainfall as they play a crucial role in the formation of cloud droplets. For rainfall, the moist air must ascend, saturate and condense. Adiabatic cooling due to an upward movement of air is one of the most important mechanisms of condensation and related precipitation including rainfall.