Yes, the battle line (close-order in two ranks) was standard, but they do have to do with light infantry tactics; and have little in common with the "Napoleonic" infantry of the 1792-1815 period beyond the close-order lines. As you mention the main difference was the speed of movement, but that evidently was considered a great distinction at the time.the civil war was fought in line... close ordered lines got nothing to do with light infantry tactics.
The only new things from Hardee's that was used was a bit faster march speed and a new manual of arms...
The "light infantry" pre-war was not limited to skirmishing, and certainly could act in close-order where necessary, see the 1825 US infantry tactics supplement for light infantry (in the back).
Scott’s 1835 tactics deleted the specific light infantry close-order drills, requiring them to use the common infantry tactics when not skirmishing. They also required all infantry to practice the skirmish drill too.
Hardee’s tactics, adopted for ALL United States foot troops by War Department General Order No. 2, 1857, further eliminated the distinction between infantry and light infantry/riflemen; Hardee's was recognized as a “Rifle and Light Infantry” system.
With the general adoption of Hardee’s for all foot troops, the system became essentially THE infantry tactics, and no distinction between infantry and light infantry was to be thereafter noticed. Note that the Confederate (Revised) editions of Hardee’s (Goetzel, Mobile, 1861-63) refers to it simply as “RIFLE and INFANTRY tactics.”
In 1862 the US Army adopted a new tactics, by Gen. Silas Casey, which was entitled, "Infantry tactics" (no distinction at all between infantry/light infantry/rifle), but it require each regiment to keep and instruct its two flank companies as "light infantry" or skirmishing companies; a sort of return to the old distinction between line and light infantry from Scott's. However, this was quashed by the War Department, which immediately ordered that part of the tactics be ignored...
General Patterson (Medal of Honor, Wilderness) in his post-war “Points on Tactics” noted the American “infantry” tactics of 1815/25/35 were copies of the French, “continued with few alterations in phraseology and details of execution in the tactics of 1815, 1825, 1835, until 1855, when Hardee's Exercises for Light Infantry were approved for the instruction of troops acting as Light Infantry…”
“In 1857 it was ordered by the War Department that all foot troops be exercised in the system of instruction for light infantry. The change from heavy to light infantry was from the more deliberate movements in common and quick time of the line manoeuvres, to the greater rapidity of movement of the light infantry system…
The company and the battalion exercises and duties of the light infantry were made the exercises and duty of all, you will remember of General Wayne's Light Division of the Continental army, and Crauford's Light Division of Wellington's army. The special duties of light infantry were those of the advanced and rear guard and skirmishers, they did what all our companies (foot) have to do now. You will find the instructions and exercises for light troops, in line and extended order, described at length in the tactics of 1825 and 1835. To fire by rank first appears in Hardee's Tactics…
Hardee's were practically the tactics of our army, and that of the Confederates also, during the Civil War, differing very little from General Casey's issue in 1863, both taken from the French Ordonnances of 1831 and 1845. The only changes of importance General Casey made, were deployments only to the front and a continuance from the system of 1815, and before and after, of the distinction between light and line infantry. This distinction was ordered by the War Department, when the tactics were issued, not to be observed, and disappears from our drill book forever after…”
Granted the close-order infantry portions of the tactics were not significantly different than the old "infantry" ones, but by most accounts the infantry lines of battle in the 1860s was not much akin to that of the Napoleonic infantry (1792-1815). First, they were quite frequently armed with rifles or rifle-muskets. Second, they moved faster, frequently at double-quick time or at a run, and finally their linear formation in battle was often similar to what James N. described above, the loose formations of the French conscript armies, or “tiralleurs en grand bandes.” (sort of a heavy skirmish line)
As General W.T. Sherman noted:
“Very few of the battles in which I have participated were fought as described in European text-books, viz., in great masses, in perfect order, manoevring by corps, divisions, and brigades. We were generally in a wooded country, and, though our lines were deployed according to tactics, the men generally fought in strong skirmish-lines, taking advantage of the shape of ground, and of every cover.” [Sherman, Memoirs, 394.]