Is EMF induced in a conducting loop moving in a uniform magnetic field with uniform velocity perpendicular to the magnetic field?
Faradays law is about changing flux in a coil. Your setup (with steady flux) and a moving coil is subject to the Lorentz force and is called Lorentz law.

Both laws do co-exist and they have little in common: Faraday is an electrodynamic law (derived from Maxwell equations), whereas Lorentz is an electrostatic law (derived from Einsteins special relativity).