Similarity manifests in various forms, including semantic similarity that is particularly important, serving as an approximation of human object categorization based on e.g. shared functionalities and evolutionary traits. It also offers practical advantages in computational modeling via lexical structures such as WordNet with constant and interpretable similarity. As in the domain of deep vision, there is still not enough focus on the phenomena regarding the similarity perception emergence. We introduce Deep Similarity Inspector (DSI) -- a systematic framework to inspect how deep vision networks develop their similarity perception and its alignment with semantic similarity. Our experiments show that both Convolutional Neural Networks' (CNNs) and Vision Transformers' (ViTs) develop a rich similarity perception during training with 3 phases (initial similarity surge, refinement, stabilization), with clear differences between CNNs and ViTs. Besides the gradual mistakes elimination, the mistakes refinement phenomenon can be observed.