Anna,
It certainly looks to me like both men were indeed in the 28th Mississippi Cavalry, and that their records are filed together in a single CMSR. The way I read the records, the elder James Hazelett was appointed Assistant Commissary of Subsistence for the regiment either when or shortly after it was organized, and remained so until his position was eliminated by Congress on July 31, 1863. All of his cards identify him as Capt. ACS F&S (Field and Staff) or Commissary Dept. Since the younger James Hazelett's records in the 10th Mississippi do not extend beyond Dec. 1861, I would assume that he was discharged from that unit prior to his 12 months of service being fullfilled on June 8, 1862, and allowed to join his father's unit on May 15. From that time until his medical discharge, he is in Company E, but detached for service in the Commissary Dept. apparently working for his father and drawing an extra 75 cents per day for that duty. All of his cards will show Private - Company E. The one document you have with both signatures is pretty unusual, and in my mind confirms all of this. J.W. Hazelett signs for his extra 75 cents per day as an "issuing clerk", while Jas Hazelett certifies the document as Capt - ACS, 28th Regt Miss Vols. If you have not already done so, look in fold3 under Confederate Records, (subheading Officers), and you will find an extensive file on James Hazelett including quite a bit of correspondence with authorities in Richmond who are questioning some of his record-keeping. Much of this takes place after he has been relieved of duty where he is referred to as Ex Capt, ACS or Late Capt, ACS.