Metal Plates moving in Magnetic Field
A metal plate moving in a magnetic field experiences a retardation force. This is commonly known as magnetic braking. This is because the metal plate is cutting the magnetic flux as it moves. The induced emf results in eddy current in the plate. The electrical energy (of the eddy current) is converted from the KE of the moving conductor. From the Principle of Conservation of Energy, the moving conductor must slow down.
Metal Plates near Moving Magnets
Metal plates (especially light ones) near moving magnets can be dragged along by the moving magnets. Why? Because the metal plates are experiencing a changing magnetic flux (due to the the moving magnets). The resulting eddy current in the metal plates produces magnetic forces that propel (rather than retard) the metal plates to chase after the moving magnets (so as to oppose the cause of induction, as according to Lenz’s Law).
Magnets Moving Near Metal Blocks
A magnet moving near a metal block can be slowed down dramatically. Why? Because different sections of the metal block experience a changing magnetic flux as the magnet approaches and leaves. The resulting eddy current (in the metal block) results in magnetic interaction that slow down the moving magnet (since magnet’s motion is the cause of induction and will be opposed as according to Lenz’s Law).