Conceptual static structure diagrams
A conceptual diagram is a static structure diagram that represents concepts from the real world and the relationships between them. It focuses on relationships and attributes rather than methods, and helps you understand the terminology in the domain area for which you are developing a system.
Class static structure diagrams
Like conceptual diagrams, class diagrams are static structure diagrams that decompose a software system into its parts. In a class diagram, however, the parts are classes that represent fully defined software entities rather than objects that represent real-world concepts.
In addition to attributes and associations, a class diagram also specifies operations, methods, interfaces, and dependencies.