Curriculum design is about the material, including facts, concepts, modes, topics, vocabulary and standards, that a student learns, including the order in which that material is presented. Instructional design, in contrast, focuses on how the material is taught, otherwise known as the pedagogical methodology. For example, curriculum design in U.S. History typically approaches the subject chronologically, but the instructional design varies widely from lecture format to student-led interactive approaches.
Common Core is the national curriculum that has been adopted by 43 states, as of 2014. This top-level curriculum defines the skills and concepts students should learn at every grade level. This curriculum is then further defined at the state, district and school level. For instance, Common Core requires the reading of "complex texts" in its curriculum, while the state of Georgia clarifies this complexity requirement for 11th graders by saying they should "analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance... for their themes, purposes, and rhetorical features" (Georgia Standards). A school in Georgia may also require students to read the Declaration of Independence. All of these are aspects of curriculum.
Instructional design is concerned with the method of delivery of the curriculum. If the curriculum topic is the Declaration of Independence, for example, one instructional method would have students complete an interactive WebQuest to define vocabulary contained in the text, to learn when and where and by whom the Declaration was signed, and analyze the persuasive rhetorical elements it contains. Another instructional design would have the teacher standing in front of the classroom giving a PowerPoint presentation while students take notes. Instruction methodologies differ widely within any given curriculum.