It seems all the two do just one thing:
breakthrough the works that we must do in our project.
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The WBS breaks down what you are building for the project into smaller, more manageable components. In most cases, the WBS should be things, not actions. The leaf level, the lowest decoposition of the WBS, is your work package. The work package, and the activities and resources--both human and materiel--are scheduled for deployment. You can include the entire WBS in the schedule or start with the work packages as your level one.
Once scheduled, the Gantt chart is a visual view of the schedule, which can be summarized to show a higher level schedule for executive review or decomposed to lower levels for a more tactical analysis.
The WBS shows what you are doing and the Gantt chart shows when you are doing it. You would use the WBS for scope control, including change management, and you would use the Gantt chart for schedule control.
The WBS is a time independent decomposition of the work requires to compete a project. After you assign owners and sequence the tasks, one output is the Gantt chart. The Gamnt is uaully at a much higher level.