Start here. This is the direct spoken answer to practice first.
Overview
Web authorization protects an HTTP route; method security protects a Java operation wherever it is invoked through the secured proxy.
Request authorization is best for route-level rules such as public, authenticated, or admin-only endpoints. Method security, enabled explicitly, protects service operations with annotations such as @PreAuthorize and also applies when the operation is called from another adapter, not only HTTP. I use request rules as the coarse boundary and method security for reusable business capabilities or resource-sensitive checks.