What is the difference between Motional EMF and Hall EMF? What is the difference between Motional EMF and Hall EMF?
 A: Motional EMF: Production of electric voltage when moving a conductor perpendicular to a magnetic field. The motion generates the voltage.
Hall EMF: Production of electric voltage perpendicular to electric current in a conductor in magnetic field that is perpendicular to the current.  The current generates the perpendicular voltage.
A: The two terms refer to two different situations where moving electrons interact with a magnetic field (although the physics of these phenomena is the same):
Motional EMF
In case of a motional EMF we are dealing with a coil moving mechanically in an inhomogeneous magnetic field (or a magnetic field through the an immobile coil is changing with time with the same effect). This generates movement of electrons in respect to the ionic lattice of the coil material, and we express the cause of this motion in terms of an EMF.
Hall EMF
In the case of the Hall EMF the electrons are driven by an electric field rather than mechanically, whereas the material itself is immobile. The presence of a homogeneous magnetic field causes displacement of the electrons in the direction transverse to the motion of the electrons, which can again be describe din terms of an EMF.
A: The Hall emf happens when a conductor carrying current is placed in an external magnetic field. Consider a copper wire connected to a battery and placed between the legs of a horse shoe magnet. In this arrangement, the magnetic field is perpendicular to the direction of current in the wire. By the Lorentz force, the electrons carrying current in the copper wire will therefore, be deflected to the outer edge of the  wire by the magnetic force. This leaves a net positive charge on the opposite edge of the wire creating a transverse potential difference across the wire. This is called the Hall emf (Hall voltage). Motional emf however, doesn't rely on the flow of electricity. It is rather caused by the motion of the conductor itself through the external magnetic field. You may as well consider that the conductor here does not carry any initial current like is needed for the Hall effect. Consider a square loop conductor with a metal rod attached within the adjacent sides of the square. This rod is free to slide from one side of the loop to the other. Let the magnetic field be directed down through the loop. If we proceed to slide the connecting rod starting from left, an induced current would be produced in the loop by Faraday's law. The flux change causing current is due to the increasing area of the loop bounded on the right by the sliding rod. What really happens is that the free electrons in the sliding rod are deflected due to the presence of the magnetic field and the motion of the conductor. The direction of this force is also given by the right hand rule and is the same force that was described above. Hence, free charges accumulate with opposite polarity on both ends of the rod creating what we call motional emf. Since the rod forms a closed loop with the remaining part of the circuit, these charges would redistribute and flow through the entire loop. In summary, _motional emf sets up current in a conductor moving in a external magnetic field. With the Hall effect however, the reverse is the case. The current is what leads to the Hall voltage for the conductor placed in a magnetic field. Both Hall emf and motional emf are caused by the Lorentz force. While charge $q$ and flux density $B$ is common to both however, $v$ is respectively the drift velocity of electrons for the Hall emf and velocity of the moving conductor in the case of motional emf.
