Creature catchers are people that, well, catch creatures, no matter if animal or monster. However, they are not hunters and never kill their targets since they are hired to specifically catch them alive. They do not catch creatures to train them and have them fight against each other (this is not Pokémon) because they, most of the time, catch creatures for clients which can vary greatly. People that want exotic/rare pets, researchers that want to study them, zoos, people that need certain ones for bioenergy and more. Independent creature catchers usually do not ask any questions but there are also those belonging to the Creature Catcher Consortium and are forced to obey its rules, including not to catch creatures for criminal organizations or to needlessly kill them.
Not all catchers are fighters, there is even a big portion of non-combatants who completely rely on traps, tricks, special gear and other means to catch them alive. Being a catcher is even harder than being a hunter because you can just kill things as a hunter but a catcher needs to make sure they can catch them alive and, as you can guess, rarely any creature likes to be caught. Catchers need to prepare for every target and there are dozens of different baits, traps and, equipment they have to prepare for the right moment since creatures vary and each one needs a different tactic to be caught. Just shooting tranquilizer ammunition at them will only work in the rarest of cases. So remember: being a catcher is not easy.
A few of them also catch creatures outside of jobs, sometimes to keep them as pets or livestock (if they have the means for that), other times to get their materials or to eat them (which is not liked by the Consortium, so it is mostly done by independent ones). Whatever they do, catchers should never forget that they are not poachers and should stand above them.