A sorcerer's job as a hunter is to effective capture, or vanquish the Nemeses that plague the world. To do so requires that the sorcerer specializes or has some degree of proficiency as a tracker in order to battle a Nemesis, or as a trapper in order to capture or bind a Nemesis. Hunters tend to work in tandem with a Researcher, who expertise and general knowledge will help locate specific Nemeses for the hunter(s) to engage in battle.
It appears that hunters are commissioned by some form of institute or organization, as seen with Artemis Institution. The institution is able to take on assignments or missions from anyone, and places it on a job posting forum where sorcerers may decide to accept. However, as shown with Alma, its possible to be a freelancer and lack a Researcher as a companion all together. In these cases, she seems to capture or slay Nemeses, then sell off the remains to the Artemis Institution for a cash reward.
Trackers are types of Hunters that specialize in combat-based spells to defeat a Nemesis through brute force, and to protect themselves from the creature's assault. Trackers seem to make their moves with the goal of either obliterating the creature, or damaging it enough to ensure for an easier capture.
Trappers are a type of Hunters that rely specialize in providing support. While this specialization doesn't tend to boast much offense, they're experts in subduing a Nemesis and keeping them bound for transportation. They can also use unique spells to help locate a Nemesis.