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The paper addresses the problem of interference modeling for wireless networks. Two axiomatic approaches are known from the literature: 1) ??standard interference functions?? proposed by Yates in 1995, and 2) ??general interference functions?? proposed by the authors in their previous work. In this paper, both frameworks are thoroughly analyzed and compared. It is shown that every function from framework 1) can be expressed in terms of framework 2). This means that recent structure results for convex interference functions, which were derived for 2), can also be applied to 1). The results provide a bridge between the frameworks 1) and 2), which were studied separately in the literature. Also, new structure results are shown in this paper. For the example of QoS balancing, it is shown that analyzing the structure of interference functions can lead to interesting algorithmic opportunities. The results are potentially useful for the development of physical-layer aware resource allocation algorithms.