For a given problem, Analysis focus on investigation of the problem and requirements, rather than searching for a solution. For example, if a new online shopping system is desired, how will the system be used? “Analysis” is a broad term, best qualified, as in requirements analysis (an investigation of the requirements) or object analysis (an investigation of the domain objects).
Design focuses on a conceptual solution that fulfills the requirements, rather than its implementation. As with analysis, the term is best qualified, as in object design or database design.
Analysis and design are best summarized by the phrase do the right thing (analysis), and do the thing right (design).