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Gauss Guns operate on the principle of a gigantic electromagnetic motor. Which uses the cycles, or Hertz of an electric motor to propel or push the projectile through a zeries of loops, with each loop accelerating the projectile a small amount. If you have a hundred loops, and each one accelerates the object 10 mph, the object will be moving at 1000 mph when it leaves the muzzle.
Gauss guns do this by overlapping magnetic fields with differing current values onto one another, each one slightly more powerful than the one before it, so there in an attractive force that aids in moving the projectile towards the next field, and it's loop.
Railguns, on the other hand, use a linear electromagnetic field, running along the length of a number of rails that run the length of the barrel. There are normally six rails, but there can be as few as three, or as many as twelve rails. The number of rails simply adds or removes from the weapon's stability and rate-of-fire. When energised, the fields run from one end of the rail to the other, and with a number of them surrounding an object, that object is pulled along by the electrical current interaction and can acheive muzzle velocities in excess of six thousand miles an hour.
The Famous Boom gun works on the same principle, but it has a wider muzzle, and combined with the extreme muzzle velocity of an object tunneling through that much atmosphere, causes a rolling peal of thunder that deafens anybody within easy reach of the weapon.