It is quite likely that they did serve with Toombs Brigade. Before the artillery was reorganized and placed under a central command, batteries were assigned to individual brigades. This proved inefficient and artillery units were reorganized and concentrated in the Spring of 1862.
Muster...by definition means the individual was present at a formal roll call of the unit.
Regulars... In the Confederacy at the beginning of the war each state was its own little country with its own little provisional army of regular forces. Units musterd in for that state's service were designated regular units to be used for the defense of the state. The Confederate Government was technically a coalition of the individual states. In order to fight the Union some sort of centralization was necessary so the individual states' governors transferred their forces to control of the Confederate States Army as Volunteer units in service to the coalition. Miledge's Regulars would indicate that the unit was originally formed as part of the state of Georgia's Provisional Army, then transferred to Confederate service. After the Spring of 1862 units that had heretofore been essentially on loan to the Confederate government for one year, became Confederate Volunteer units for three years or the duration of the war.
In the Union Army Regulars meant units that had existed before the war in the Regular professional U.S. Army. Volunteers were units raised by the individual states and sent to Federal service by their governer to serve the Union for the period of the war. By and large Union volunteer units ath the start of the war were only 90 day regiments. The war lasted longer that they figured on so when the 90 day enlistments were up, the units were either re-enlisted for 3 years or were disbanded.
Enlisted man is just that. A soldier enlisted for a definite period of time. In contrast to a commissioned officer, who served as long as needed, sometimes indefinitely.
Hopefully I have answered your questions abd not confused you.