The literature on definitions of security based on causality-like notions such as noninterference has used several distinct semantic models for systems. Early work was based on state-machine and trace-set definitions; more recent work has dealt with definitions of security in two distinct process algebraic settings. Comparisons between the definitions has been carried out mainly within semantic frameworks. This paper studies the relationship between semantic frameworks, by defining mappings between a number of semantic models and studying the relationship between notions of noninterference under these mappings.