Tracer tool is used to debug flows, data transforms, activities, services, parse rules, and declarative rules. It provides full debugging facilities, including step-by-step execution, breakpoints, and watch variables.
UI inspector tool is used to view the hierarchy of artifacts in your application UI. Inspect the harnesses, sections, containers, layouts, cells, and properties of your application at runtime. Make UI adjustments at runtime and publish or discard changes on the fly.
You would use Live UI to examine the current state of the UI, and determine which rules are used to generate the current form displayed in the browser.
You would use the Tracer to identify all of the rules used to execute a process step and display a UI form. The Tracer would help you to identify the sequence of failures in rule execution that lead to an error message appearing on-screen.