This one seems to have two parts so I'll break it out like that.
Test Leadership/Management Reports:
- Functional Test Report (RTM*)
- Regression Test Report (RTM* sometimes combined with functional report)
- Interface Test Report (RTM* optional depending on interfaces)
- Security Test Report (RTM* optional depending on security requirements)
- Performance Test Report (RTM* optional depending on performance requirements/needs)
- Failure/Defect Report (Often embedded inside the corresponding report listed above but delineates failures and fixes including defects and during which type of test it occurred.
- Test Readiness Review Package (functional/regression/boundary/interface/performance/security/etc...) usually to justify software is ready to release. This takes many different forms, but it usually entails all the test reports summary rollup into the big picture as is the minimal test deliverable to accompany software releases. The nuances often depend on the management processes, the application under test, and the quality needs.
Individual Testers Reports/Expectations:
- Test Execution runs including pass/fail and any defects found. This is for any test type being executed.
- Full defect articulation in approved ticketing system
- Test Case Reviews by peers with audit trail for the review taking place
- RTM* to test case mapping to ensure that all requirements are met via test cases
*Requirement Traceability Matrix - Requirement definition varies depending on the Development Methodology (waterfall - traditional requirement text, SCRUM - backlog items with acceptance criteria, Kanban - ticket description, etc...)
Follow your leadership/management direction, but every good QA engineer keeps track of his or her work, results, and logs defects accordingly. Whatever format the tracking takes place a manager should be able to get the update on the software test status with enough details to meet the expectations of assigned work. Don't be caught in the "I think I did that" or "I think I may have tested that enough" situation. If your project company is really lax in this fine, but it would be good for a career point to be aware of the goal of the reports in the industry.