From my understanding prior to the Confederate reorganization the units were generally referred to as the 21st Regiment Alabama. After the reorganization in 1862 the unit was known as the 21st Alabama Infantry. This may have been referred to this way in the eyes of the Confederate AGIO. I agree this is splitting hairs and depending upon which reports the reader reads they are listed both ways during the course of the war. If you were going to mention them at Fort Gaines it might be a safe bet to refer to them as the 21st Alabama Infantry although I don't think anyone will find fault with them being referred to as the 21st Alabama Regiment.

I ask the same question a while back on another Confederate unit and that was the answer given to me.