Alloy is a textual modeling language for structures and behaviors of software designs. The Alloy Analyzer provides various analyses making it a popular light-weight formal methods tool. While Alloy models can be analyzed, explored, and tested there is little support for comparing different versions of Alloy models. We believe that these comparisons are crucial when trying to refactor, refine, or extend models. In this work we present an approach for the semantic comparisons of Alloy models. Our pair-wise comparisons include semantic model differencing and the checking of refactoring, refinement, and extension. We enable the semantic comparison of Alloy models by a translation of two versions into a single model that is able to simulate instances of either one or of both version. Semantic differencing and instance computation require only a single analyses of the combined model in the Alloy Analyzer. We implemented our work and evaluated it on over 600 Alloy models from different sources including version histories. Our evaluation examines the cost of semantic comparisons using the Alloy Analyzer.