We report on the electric field dependent carrier dynamics and optical absorption in nonpolar a-plane GaN-based quantum heterostructures grown on r-plane sapphire, which are surprisingly observed to be opposite to those polar ones of the same materials system and similar structure grown on c-plane. Confirmed by their time-resolved photoluminescence measurements and numerical analyses, we show that carrier lifetimes increase with increasing external electric field in nonpolar InGaN/GaN heterostructure epitaxy, whereas exactly the opposite occurs for the polar epitaxy. Moreover, we observe blue-shifting absorption spectra with increasing external electric field as a result of reversed quantum confined Stark effect in these polar structures, while we observe red-shifting absorption spectra with increasing external electric field because of standard quantum confined Stark effect in the nonpolar structures. We explain these opposite behaviors of external electric field dependence with the changing overlap of electron and hole wavefunctions in the context of Fermi's golden rule.