If your Jenkins agent is running as a service, then that may cause different behaviors if your tests depend on interacting with a user interface (like Selenium tests, or web browser driven tests).
If your Jenkins agent is running as a different user, and your tests depend on a specific user, that could cause different behavior in Jenkins than in the user environment.
If your Jenkins agent is running on a different Windows version and your tests have Windows version requirements, that could cause failures.
Mark Waite