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In this paper we put into practice the concept of compatibility and we present a classification of two IBE-related schemes, the Identity-Based Encryption (IBE) and the Certificate-Less Encryption (CLE). An innovative implementation of a compatible IBE and CLE system was developed in order to support different encryptions on-the-fly based on the user’s needs at a specific moment. Motivated from the fact that there are numerous theoretically efficient IBE-related schemes in the literature overshadowing the benefits of traditional public key encryption (PKI) schemes, they did not, in any important way implemented into practice, as the widelyused PKI. The question is why this is the case since IBE solves a number of problems associated with PKI. Therefore, the controversial issue concerning the widespread use of IBE schemes into practice and the issue of compatibility between IBE and CLE are discussed in this paper. These real problems hinder the wide use of IBE. However, 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 is important. 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.