While numerous studies have analyzed the conceptions probed by the Force Concept Inventory (FCI), assessments dedicated to electricity and magnetism lack similar analyses. This paper investigated the conceptions explored by the Brief Electricity and Magnetism Assessment (BEMA) and the Conceptual Survey of Electricity and Magnetism (CSEM) using exploratory factor analysis techniques. Exploratory factor analysis (EFA) was performed on both assessments using 5368 and 4941 postinstruction student responses for the BEMA and CSEM, respectively. A 6-factor EFA generated model was found for the CSEM, and was fit against another sample of 4964 student responses using confirmatory factor analysis to supply evidence for the possible generalizability of the model. The 5-factor EFA generated model for the BEMA could not be fit against another sample when trying to check for generalizability. The EFA generated factor models for the BEMA and CSEM were then compared and found to be similar in conceptual content, with the exception of one or two factors. Thus, from a factor analysis perspective, the BEMA and CSEM were found to be similar in conceptual content as revealed by student responses. With a better understanding of these electricity and magnetism assessments, future research into this domain of physics will then be able to make stronger conclusions based on students' results within these assessments.