Is it correct to say that they do the same thing (examining costs from past to present), with the differences being Cost & Usage Report is more detailed, while Cost Explorer does visualization and also includes forecasting?
Microsoft describes the two this way:
"AWS Cost Explorer lets you explore your AWS costs and usage at both a high level and at a detailed level of analysis, and empowering you to dive deeper using a number of filtering dimensions (e.g., AWS Service, Region, Member Account, etc.) AWS Cost Explorer also gives you access to a set of default reports to help you get started, while also allowing you to create custom reports from scratch." *
"The AWS Cost & Usage Report is your one-stop shop for accessing the most detailed information available about your AWS costs and usage. The AWS Cost & Usage Report can be generated at an hourly, daily, or monthly granularity." *