Using a plane-wave pseudopotential method we investigate the electronic structure of free-standing and of AlAs-embedded GaAs quantum dots, wires, and films. We predict that (i) the confinement energy of the valence-band maximum (VBM) is larger in AlAs-embedded than in free-standing quantum structures, because of the zero-confinement character of the VBM wave function in the latter case; (ii) small GaAs quantum structures have an indirect band gap, whereas large GaAs quantum structures have a direct band gap; (iii) the conduction-band minimum of small free-standing quantum structures originates from the GaAs X1c valley, while it derives from the AlAs X1c state in AlAs-embedded quantum structures; (iv) the critical size for the direct/indirect crossover is larger in embedded quantum structures than in free-standing quantum structures.