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This paper introduces the concept of compatibility and presents an extended classification of two IBE-related schemes, the Identity-Based Encryption (IBE) and the Certificate-Less Encryption (CLE) in order to implement compatible systems. It cannot be denied that IBE, which can be extended to support a plethora of encryption models, gains widespread adoption day by day as it solves problems within conventional public key schemes and it results in a simplified key management, making it much more lightweight to deploy. Based on the fact that a number of different encryption schemes stemmed from IBE, an implementation of an IBE-related compatible system enables a number of different encryptions on-the-fly based on the user’s needs at a specific moment. Our approach categorizes known concrete constructions from two IBE-related types into classes and analyzes similarities concerning public settings, used keys, protocol structures and provided model of provable security. Therefore, we consider compatibility issues between CLE and IBE and we conclude that a significant number of them are closely related. Therefore, the concept of compatibility can be put into practice.