Answer set programming  is a  declarative programming paradigm used in formulating combinatorial search problems and implementing distinct knowledge representation and reasoning formalisms. It is common that several related and yet substantially different answer set programs exist for a given problem. Uncovering precise formal links between these programs is often of value. This paper develops a methodology for establishing such links. This methodology relies on the notions of strong equivalence and conservative extensions and a body of earlier theoretical work related to these concepts. We use distinct answer set programming formalizations  of an action language C and a syntactically restricted action language C+ to showcase the results. As a by product we  make the frequent claim occurring in the literature, namely, the action language C is the immediate predecessor of C+,  mathematically precise. Indeed, we illustrate that an action description in C+ limited to the syntactically allowed expressions by C is also  an action description in C and the other way around.