Michael Crumplin's The Bloody Fields of Waterloo: Medical Support at Wellington's Greatest Battle goes into great detail on the role of surgeons, assistant surgeons, etc.
Regimental Surgeons: "Acted as general practitioners for their battalions". They provided the primary care for the soldiers and in a battle would usually set up an aid station close to the front lines to treat the wounded. The seriously wounded would be evacuated from the aid station to the field hospitals. (page 53)
Regimental Assistant Surgeons: were authorized in battalions of more than 500 men. (page 56)
Staff Surgeons: worked in the hospitals. There were also assistant staff surgeons. (page 49)
Surgeon Major: was a rank within the Foot Guards regiments and rarely used until the 1820s. (page 48)