The ability for analogical reasoning, such as understanding that the relationship between two items is similar to the relationship between two other items, has long been considered to be unique to humans. Whether and to what extent non-human animals can recognize such relational analogies is still debated. We tested such abilities in two groups of budgerigars with a diverse set of item categories in which the figures of the stimuli were quite different in nature (size, color, shape, geometric type, and number). Budgerigars trained to discriminate two identical figures from the same two figures differing in size, generalized the discrimination to test stimuli belonging to the novel categories, demonstrating the spontaneous use of analogical relations. In contrast, budgerigars trained to discriminate two circles that were either the same or different in color seemed to generalize to novel stimuli by perceptual rather than conceptual similarity. The results thus demonstrate the spontaneous emergence of perceiving analogical relations in budgerigars of a nature beyond that demonstrated in previous studies of non-primate species. However, the results also show that whether budgerigars generalize a relationship by perceptual or conceptual similarity seems dependent on the nature of the training stimuli.