Static analysis is the process of using automation to analyze the application’s code base for known security patterns. It uses different methods, such as following data from it source (input) to its sink (output) to identify potential weaknesses. It also uses simple search methods in an attempt to identify hard-coded values, like passwords in the code. Automated tools struggle at finding business logic or authentication/authorization flaws.
Code Review is a much larger project where both automated and manual techniques are used to review a code base for potential security risks. A code review may incorporate a static analysis component to quickly scan for some types of vulnerabilities. The manual part of the secure code review involves a person looking at the code to identify flaws that automated scanners cannot. For example, they may look at the authentication logic looking for potential logic flaws. They may also look to identify other authorization or business logic flaws that the automation is challenged to find.