Level, flat, plane, plain, even, smooth, flush are comparable chiefly as applied to surfaces and as meaning having a surface comparable to that of a perfectly calm body of water with no part higher than another.
Something is level whose surface, from every point of view, lies on a line corresponding to or parallel with that of the horizon. But level is also applicable to an adjacent surface lying in exactly the same plane. In extended use level implies an equality of parts, or of one thing with another, so that there are no manifest fluctuations or irregularities; thus, to speak in a level voice is to speak without the variations in pitch or voice volume that indicate imperfect self-control; to keep a level head is to keep free from distracting excitement.
Something is flat (see also INSIPID ) which is marked by absence of noticeable curvatures, prominences, or depressions, whether it lies in a horizontal plane or not. But flat may apply to something that lies directly upon or against a flat surface.
In extended use flat applies sometimes to what is so lacking in variation or variety as to be monotonous or to what gives no ground for doubt or for difference in description because direct, pure, complete, or unqualified or to what is fixed or absolutely exact. Something is plane or plain which is flat and usually level.
Plane is more usual in technical and mathematical use and more often applies to angles, curves, or figures (as triangles, rectangles, and pentagons) all points of which lie in the same real or imaginary surface so that if any two points be taken within the boundary lines of the angle, curve, or figure, the straight line joining them lies wholly within that surface; thus, plane geometry, which deals with plane angles, curves, and figures, is distinguished from solid geometry <the plane sides of a crystal>
Plain is much less frequent in adjectival use and applies chiefly to the ground.
Something is even (see also STEADY ) which exhibits a uniformity of all the points either of a plane surface or of a line so that the surface's flatness or levelness or the line's straightness is observable.
Something is smooth that exhibits perfect evenness of surface, as though polished, rolled, or planed free from the slightest traces of roughness or unevenness.
A surface or a line is flush that is in the same horizontal or vertical plane or forms a continuous surface or line with another surface or line.