Here are the two you note, two separate individuals. There are some four or five more John Morrison's in Louisiana units

John Morrison, Private, Captain William Monahan’s Company, (Co. B, Irish Brigade), 6th Regiment Louisiana Infantry,* enlisted June 14, 1861 at Camp Moore by Lieut. Phifer for the war, wounded at Winchester, June 14, 1863, absent August 31, 1864, Detailed in Richmond, Va., guard at 4th Division, Gen. Host., Camp Winder, Richmond, Virginia December 30,1864, captured at Jackson Hospital, Richmond, April 3,1865, born in Scotland, Laborer, resident of New Orleans, age 30 on enlistment, single

* This company subsequently became Company F, 6th Regiment, Louisiana Infantry

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John Morrison, Private, Capt. L. D. Nicholls’ Company, 8th Regiment Louisiana Volunteers,** enlisted June 19,1861 at Camp Moore by Lieut. Phifer for the war, wounded near Fredericksburg, Va. May 4, 1863, captured at Petersburg April 3, 1865, released June 14, 1865 at Hart’s Island, N. Y. Harbor, resident Ascension. La., dark complexion, black hair, grey eyes, 5’ 10-1/2”, born in Ireland, Mason single, 47 years old on enlistment, resident of New Orleans

** This company subsequently became Company K, 8th Regiment Louisiana Infantry

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Louisiana