Recently, the problem of measuring the conflict between two bodies of evidence represented by belief functions has known a regain of interest. In most works related to this issue, Dempster's rule plays a central role. In this paper, we propose to study the notion of conflict from a different perspective. We start by examining consistency and conflict on sets and extract from this settings basic properties that measures of consistency and conflict should have. We then extend this basic scheme to belief functions in different ways. In particular, we do not make any a priori assumption about sources (in)dependence and only consider such assumptions as possible additional information.