The tactical instruction of army units provided modes for passing over routes of march in whatever order was suitable. Were it possible, they might have marched generally in "column of companies"... With each of a regiment's ten companies in line, one behind the other, ready to wheel into line of battle in whatever direction on command...
But a column of companies on the march required a very wide road. And the roads in America were generally not that wide, and the fields were constrained with fences, and the terrain generally wooded.
In the Southwest, during the War with Mexico, there were places where the roads were wide enough to march in column of companies evidently...
But back east, the campaigns of the war of 1861-65 were generally fought in a largely wooded region. Consequently the roads generally too narrow for a column of companies.
So where possible, units were to march in a column of platoons, or half-companies (half the width of the companies). This also required a somewhat wide road. Here's a column of platoons...
However, again, the roads were generally too narrow for column of platoons. The customary mode, consequently, was to march the line "by a flank" (the line facing left or right, and marching). When they did so, the men of the two ranks "doubled"... so moving by a flank, the column was four men abreast... besides the officers and file closing N.C.O.s. By this means, the length of the line did not straggle too much beyond the length of the line of battle (which they could quickly form by undoubling and facing to the left or right, etc.)
Where a defile in a route was even more narrow, the unit marching by a flank could "undouble" and move in two files abreast...
Or form in single file where necessary to pass through the narrowest defiles...