An implicit ambiguity in the field of prediction-based decision-making regards the relation between the concepts of prediction and decision. Much of the literature in the field tends to blur the boundaries between the two concepts and often simply speaks of 'fair prediction.' In this paper, we point out that a differentiation of these concepts is helpful when implementing algorithmic fairness. Even if fairness properties are related to the features of the used prediction model, what is more properly called 'fair' or 'unfair' is a decision system, not a prediction model. This is because fairness is about the consequences on human lives, created by a decision, not by a prediction. We clarify the distinction between the concepts of prediction and decision and show the different ways in which these two elements influence the final fairness properties of a prediction-based decision system. In addition to exploring this relationship conceptually and practically, we propose a framework that enables a better understanding and reasoning of the conceptual logic of creating fairness in prediction-based decision-making. In our framework, we specify different roles, namely the 'prediction-modeler' and the 'decision-maker,' and the information required from each of them for being able to implement fairness of the system. Our framework allows for deriving distinct responsibilities for both roles and discussing some insights related to ethical and legal requirements. Our contribution is twofold. First, we shift the focus from abstract algorithmic fairness to context-dependent decision-making, recognizing diverse actors with unique objectives and independent actions. Second, we provide a conceptual framework that can help structure prediction-based decision problems with respect to fairness issues, identify responsibilities, and implement fairness governance mechanisms in real-world scenarios.