The difference is the one below is a first hand account written just one month after the event.
Appears these are both shaggy dog stories or, at the least, there was an embellishment of the true circumstance.
AMERICAN CITIZEN [CANTON, MS], July 6, 1861 - November 6, 1863
A Baby Found on the Battle Field of the
Hatchie.
Extract of a letter from a private soldier in the 14th Illinois regiment:
Bolivar, Tenn., Nov. 10.
Let me relate to you a touching little incident, that will doubtless strike you a little strange. I thought it strange when I witnessed it; my comrades thought it "passing strange," if not wonderful. At the battle of Hatchie, when the conflict was waging fiercest, upon advancing midway between the contending forces, we found, what do you think? Not a masked battery—not an insidious trap, inviting but to destroy—not any visible engine of death—but a sweet little blue eyed baby, fresh from the womb of the mother that groaned and gave it birth. Sweet little thing, as I saw it there, hugging the cold earth, its only bed—the little tear on its cheek,
"That nature bade it weep, turned
An ice-drop sparkling in the morning beam"
Unalarmed 'mid the awful confusion of that tearful battle, with the missiles of death lying thick about it, and crowding close upon existence, yet unhurt, it seemed a wonderful verification of the declaration, "Out of the mouth of babes and sucklings I will ordain wisdom." That little "child of war," as it lay in its miraculous safety, seemed to say to me those words of profound instruction, "My helplessness and innocence appealed to God, and he preserved me in the midst of this wrecking carnage. If you will make your plain to Heaven, God will preserve your poor bleeding country."
Little child of destiny, born amid the flash of musketry, the thunder of cannon, and clash of arms, I will watch your course through life, and witness whether an existence so auspiciously begun, will pass by the masses unnoticed, and end without leaving a name "damned to everlasting fame!" Who would suppose that in the wild fierce battle of the Hatchie, where the field was strewn with the dead, and the shrieks and groans of the wounded rent the heavens with agony, a great army would pause in the thickest of the conflict to save harmless a helpless child? Yet the brave 14th that never yet has quailed in battle, did pause, and the officer of the regiment ordered our "little baby" to be carried to headquarters and tenderly cared for.
I remember of having read somewhere in Grecian history a story something like the one I have related. A little child was found on the battle field, and by an infuriated soldiery trampled in the dust. After the battle the victorious general said: "But for the blood of the little child that mars it, our victory would be complete." Thank God, the blood of no little child mars our victory.
The next day after the battle "our babe" was brought before the 14th, and unanimously adopted "child of the regiment." Three or four days later, strange as it may seem, a poor heart stricken, poverty pinched mother, came searching the battle field in quest of her child. My dear _____, imagine if you can the wild exclamation of thanksgiving that burst from that poor woman's heart, when informed that her child had been rescued, and with a mother's tenderness cared for. I saw the mother receive her child, heard her brief prayer for the soldiers who saved it, and, with the blessings of a thousand men following her and hers, she took away
"Our little baby—
Little blue eyed, laughing baby."