Conceptual design seeks to deliver design concepts that implement desired functions. Function and behavior are two dominant terms used in the research of this design phase. However, there are still some fundamental ambiguities and confusions over their representation, which have greatly hindered the interchange of research ideas and the development of design synthesis strategies. For conceptual design of mechanical products specifically, this paper attempts to clarify these ambiguities. It classifies function as purpose function and action function and relates them to the different levels of design hierarchy and abstraction. It distinguishes between semantic and syntactic representations of function and behavior and summarizes basic representation schemes. It also proposes an input–output action transformation scheme for semantic function representation and an input–output flow of action scheme for semantic behavior representation. Based on these discoveries, a refined framework is proposed for conceptual mechanical product design, where a function–decomposition–mapping process is elaborated to demonstrate the necessities and usefulness of the presented work.