Definitions

Vertical Line: The line that follows the direction of gravity
Level Surface: A curved surface, perpendicular to the local gravity direction, at every point.
Level Line: A line perpendicular to the direction of gravity at each point along the line, and is a curved line. Contained in a Level Surface.
Horizontal Plane: A plane perpendicular to the direction of gravity at a point. A flat surface
Horizontal Line: A straight line perpendicular to the direction of gravity at a point