【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.