SrAl2O4:Eu,Dy is presumably the best known persistent luminescent phosphor. At room temperature, its green emission remains visible for hours after switching off the excitation. It is known that upon lowering the temperature of the phosphor a second photoluminescence emission band arises in the blue part of the visible spectrum, although its origin is still the subject of discussion. In this paper we thoroughly study the origin of both emission bands in SrAl2O4:Eu,Dy and we attribute this to europium ions substituting for the two different Sr sites in the phosphor's monoclinic host lattice. The photoluminescence properties, the thermal quenching behavior, and photoluminescence lifetime of both emission bands are investigated. A lanthanide energy level scheme is constructed for both sites. Using an integrated approach, i.e., combining charging, afterglow, and thermoluminescence measurements in the same run, we study the charging or trap filling processes in SrAl2O4:Eu,Dy upon excitation with site selective excitation wavelengths and at different temperatures. We show that trap filling is a thermally activated process when the green emitting center is excited at 435 nm. Furthermore, we also demonstrate that the distribution of filled traps after charging depends strongly on the excitation wavelength and thus on which Eu2+ center has been excited. This suggests trapping of the electron close to the ionized Eu2+ ion, without full delocalization to the conduction band during the trapping process. Finally, the quantum efficiency of the persistent luminescence is estimated at 65 (+/−10)%.