Searched Booth's "Records" and the NPS online Index of the CMSR for Alex PELLERIN:
(1) A. PELLERIN, a member of Captain LeGardeur, Jr.'s Company, Orleans Guard Battery, Louisiana Light Artillery reported as "on parade" November 23, 1861.
This is a state militia service record. A Confederate unit of the same name composed of volunteers from this state militia unit was organized for Confederate service on March 6, 1862 at New Orleans and sent to Corinth, Mississippi. Dr. Bergeron's "Guide" contains an excellent thumb nail sketch of the subsequent history of this unit.
There is no indication in Booth's "Records" that this soldier volunteered for the Orleans Guard Battery organized for Confederate service on March 6, 1862. The Orleans Guard state militia regiment remained more or less active until the Federal occupation of New Orleans at the beginning of May 1862. I am not sure what happened to the state militia artillery since they would likely have had no guns. The CMSR might give you additional information, but the NPS Index only tells us there is a record under that name.
(2) Alex L. PELLERIN, 1st Sergeant, Company I, 3rd (Harrison’s) Louisiana Cavalry, reported into the Federal parole center at Natchitoches, Louisiana to be accounted for and released on parole under the terms of surrender for the Confederate Trans-Mississippi Department. He was released on parole on June 6, 1865. His place of residence was in St. Mary’s Parish.
(3) A. PELLERAN, Private, Company A, 7th Louisiana Cavalry reported into the Federal parole center at Franklin, Louisiana and was released on parole on June 10, 1865. His place of residence was in St. Mary’s Parish. This record is part of a "family cluster" as there are two more paroles with this surname spelling in Company A, 7th Louisiana Cavalry
(4) A. PELERINE (PELLERIN?), Sergeant, Company G, 1st Louisiana Heavy Artillery (regulars). Enrolled August 6, 1863 at Mobile, Alabama. Company muster rolls covering January through October 1864 show he was detached to a company of the 21st Louisiana Battalion acting as Ordnance Sergeant. The company muster roll for March & April 1865 show him detached service to the Ordnance Department by Special Order No. 94, District of the Gulf dated April 14, 1865. After the surrender of the Department of Alabama, Mississippi, and East Louisiana, he was released on parole at Meridian, Mississippi on May 12, 1865. His place of residence was given at New Orleans.
Given family traditions, place of residence, etc., it would be reasonable to presume that Items #1 and #4 represent the same soldier. Dr. Bergeron’s “Guide” provides an excellent thumbnail sketch of the history of all of these units. I recommend you get a copy of the CMSR for A. PELLERIN in the Orleans Guard Battery in the off chance that this will show that he was enrolled in Confederate service on March 6, 1862 at New Orleans.
Hope all this helps!