Diagrams are ubiquitous in physics, especially in physics education and physics problem solving. Physics problem solvers may generate diagrams to orient to a scenario, to organize information, to directly obtain an answer, or as a tool of communication. In this study, we asked 19 undergraduate and graduate physics majors to answer 18 multiple-choice (MC) physics questions and then complete six diagramming tasks of situations similar to six of the MC problems: the MC problems contained no prompting regarding diagrams, while the diagramming tasks explicitly asked participants to carefully generate diagrams. This prompting placed participants in one of two epistemic frames, problem solving or communicating, which allowed us to explore which elements and features the students include (or not) in diagrams generated when students are working within these two frames. By comparing students' spontaneously generated diagrams to their prompted diagrams, we found differences in size, accuracy, and amount of detail in unprompted problem-solving diagrams and prompted communicating diagrams. We also looked at correlations between the presence and features of unprompted diagrams with participants' answer choice. Looking at the different cohorts (e.g., lower-division undergraduate and graduate students), we found that the differences in diagramming between cohorts were generally smaller than the differences within a cohort. We also explore implications for teaching and research.