Self-assembled strain-free GaAs quantum dot and quantum ring structures grown by droplet epitaxy were investigated by the RHEED technique. The temporal evolution of these nanometer-scale objects were tracked in situ manner during the growth process. The initial stage of the surfaces was the same for both kinds of quantum objects. We have compared step by step the RHEED pattern in direction in the case of both quantum objects. After the Ga deposition the pattern becomes diffuse. Almost at the same time with the offering of arsenic the RHEED pattern changed from diffuse to spotty and later changed slowly to spots with chevrons in case of the quantum dot. In case of the quantum ring the situation is quite different. The pattern, which consists of streaks and spots, evaluate slowly and continuously. The different patterns and their different temporal evaluations can be explained with the shape and the kinetic of development of different quantum objects.