Rotatory motion is simply the motion of anything in a circle around an axis. So a fan is in rotational motion. The London Eye is also a device in rotational motion. Every point on the object rotates around an axis of rotation. And the number of turns around the axis per unit time is the same for every point on an object in rotational motion. So every point on the London Eye and a fan, make the exact same number of revolutions around the axis of rotation.
In linear motion , every point in the object is moving in the same direction with the same speed, that is every point has the same velocity ( speed + direction). However in rotational motion, every point does not have a the same speed ( the points farther from the axis have a higher speed, and the points closer to the axis have a slower speed), and not every point’s movement is in the same direction. If the London Eye is moving clockwise, then the top point is moving towards the right, and the bottom most point is moving towards the left, so clearly every point does not have the same direction of movement.