Project Objectives are typically higher level than individual Stakeholder Requirements. They usually come first, created up-front in the Project Initiation phase before you've delved in to individual Stakeholder Requirements.
Stakeholder Requirements are lower level and more specific that Project Objectives. They'll carefully define the needs of the various stakeholders. Remember that these can include Functional (eg gather feedback from users) and Nonfunctional (eg responsive design) requirements.
You'll find throughout the progression of a Project that many "outputs" are re-workings of previous "outputs" at either a lower level of detail, or with more clarity and certainty than before. This is because as a Project progresses you are continually gathering more information that help define the details of the project itself. You start broad (vision / objectives) and end specific (requirements / solutions).