In this equidistant cylindrical map, all
green lines are equally long; however, actual world distances
(in km, actually measured along the red geodesics) between the
ends of each line vary enormously.
Four blue graphic scales are supplied; for this projection, each horizontal one is only useful along its specific parallel (i.e., if it were a ruler, one could slide it horizontally only and still take precise measurements) or the one symmetric opposite the Equator; the vertical scale is valid anywhere. None will give meaningful results if rotated. 
Any practical map, spherical or flat, shrinks Earth features down to a manageable size. The general rate of reduction, the scale, can be expressed graphically or numerically. The latter case is usually a fraction; for instance, on a 1:100000scale map, two points separated by 1 unit could represent two cities actually 100000 units apart; 1 centimeter on the map means 1000 meters on Earth. With a scale 10 times "larger", 1:10000, one inch on the map corresponds to 10000 inches on Earth, and so on. Therefore, if the same region is presented in different maps, smallerscale versions can be more portable but probably less precise and detailed.
A graphic scale is, at a minimum, a small "ruler" tagged with absolute distances and directly superimposed on the map. Although a distance evaluation requires two measurements (one for the ruler, another for the map itself), it has an important advantage: the map may be reproduced at different sizes with no modifications, while a numerical scale must be recomputed for each size. Graphic scales are especially useful for electronic devices like computer screens (whose resolution/physical size ratios are seldom correctly calibrated) and presentation slides (where the display's dimensions depend on the distance to the projection screen).
Either graphic or numeric, only on a true globe a scale can be directly applied to any pair of points on its surface. In flat maps, most likely the reduction rate, or scale factor, is not constant, changing with direction and location. Especially, it may be nonlinear: the length ratio of two segments of a line on the map is not the same for the corresponding segments on Earth. Finally, the shortest distance between two points on a sphere is rarely represented by a straight line on a flat map, and measuring distances along an arbitrary (not always marked) curve is not a straightforward procedure.
Thus, depending on the range of the mapped region (the larger, the greater will be distance distortions), neither numbers nor rulers can be reliably used without knowledge of the projection's properties; they both can be just misleading.
The outer edges of some azimuthal, cylindrical, conic and flatpolar pseudocylindrical provide some striking examples of distance distortion, as single points on Earth become lines on the map; in general any fullworld map's edge distorts distances because points are projected twice in places far apart.
Some standard lines (marked in proportion 1:2:3) in selected projections  

Lines on the map, straight or not, with constant, linear scale (with length proportional to that of corresponding lines on Earth) are lines of true scale or standard lines. Map projections with a welldefined, nontrivial set of standard lines are sometimes referred to as equidistant. Some wellknown examples are the equidistant cylindrical (in the normal aspect, all meridians and one or two parallels are standard), azimuthal equidistant (in the normal aspect all meridians are standard), and the conic equidistant (in the normal aspect, all meridians and one or two parallels are standard).
A common source of gross mistakes is assuming a circle drawn on a map represents the same range of distances as the corresponding shape on Earth. This only happens if the all straight lines radiating from the circle's center are standard lines.