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A clear terminology is essential in every research discipline. In the context of ESOA, a lot of confusion exists about the meaning of the terms emergence and self-organisation. One of the sources of the confusion comes from the fact that a combination of both phenomena often occurs in dynamical systems. In this paper a historic overview of the use of each concept as well as a working definition, that is compatible with the historic and current meaning of the concepts, is given. Each definition is explained by supporting it with important characteristics found in the literature. We show that emergence and self-organisation each emphasise different properties of a system. Both phenomena can exist in isolation. The paper also outlines some examples of such systems and considers the combination of emergence and self-organisation as a promising approach in complex multi-agent systems.