Adaptive systems are a common and trendy concept within the field of Computer Science. Scientific literature about this topic includes a wide spectrum of systems from different computer science domains, starting from automation till HCI. When someone reviews the scientific literature with keywords, e.g. adaptation, adaptive system, there is a huge amount of researches and it is difficult to link together similar researches. The contribution of this paper lies in (1) defining four types of adaptive systems based on system and environment interaction view, which can be applied to any adaptive system; (2) proposing environment-system-user interaction view - the list of core concepts of adaptive system and extended list with user-oriented aspects; (3) describing possible adaptation results and formalize the main target of adaptation. The environment-system-user interaction view can serve as a basis for classification of adaptive systems and building a clear understanding about different types of adaptive systems and their essential (not all) differences. The proposed adaptive system types and core concepts are illustrated with examples.