The bullet, if fired perfectly horizontal will have the same time of flight, regardless of the caliber or how fast the bullet is shot. In this condition, if you dropped a bullet from the same height at the muzzle at the same time the gun was fired, both bullets will hit the ground at the same time.

That being said, when you sight in your rifle, the bullet is not fired perfectly horizontal to the ground. The barrel is angled slightly upward to provide a ballistic trajectory and have the bullet impact the target at the sight plane at the specified zero distance.

For something like a .270 Win zeroed at 200 yards, when the bullet is fired, at the muzzle it is about 1.5" low (distance between the muzzle and the center of the scope optics. The bullet will continue to rise, passing the optic plane just shy of 50 yards. It will continue to rise until it hits it's ballistic apex at about 120 yards. At this distance the bullet is about 2" high. It will start to drop from this point on, passing through the sight plane at 200 yards (zero mark) and dropping progressively faster as you go out. At 500 yards, the bullet is about 50.8" below the sight plane.