When Orry & Charles rescue George from Libby Prison, we see that Charles is wearing the 1-star collar insignia of a Confederate Major, indicating he has been promoted. Later in the same episode, we see Charles wearing the 3 rank stripes of a Captain, and is addressed as such.
When Charles meets Orry at his office to help him rescue George from Libby Prison, we see that Charles has been promoted to Major, as he is wearing a single star on each collar of his Confederate Army uniform. After helping George escape, Charles returns to his unit and is wearing the three stripes of a Captain. Later, one of his subordinates addresses Charles as "Major", and at the Civil War's end, Charles is wearing Major's rank insignia again.
Lieutenant General Ulysses S. Grant's Chief of Staff was Brevet Major General John A. Rawlins, portrayed by an uncredited actor who was elderly and clean-shaven. The real-life John Rawlins was 33 years old in 1864, had a full beard, and suffered from tuberculosis (which gave him a persistent hacking cough), which claimed his life only five years later.