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These are NOT replacements for each other. Gazebo, ROS, and MoveIt serve completely different purposes.
Gazebo is a simulator, it doesn't do any motion planning. ROS is (in this context) the middleware that allows gazebo to talk to other software. MoveIt is a motion planning framework that uses ROS to talk to Gazebo.
If you want to do motion planning, use moveit.
If you want to test these motion plans without an actual robot, replace that robot with a simulated one in gazebo.