Craft Users are humans with a witch gene, capable of using different kinds of powers. This gene travels through family and herits from parents to children. But not all children of of witches gain the ability to use witch craft. Those just simply carry the gene and are called Seeds. And a seed's child can gain the use of witch craft.
A witch is a human using their craft harmfully and being a danger to humanity. A witch is a different from a Craft user in a sense, that their powers have been fully awakened. Which usually causes them to hurt others with their powers without caring one bit. It is also possible that from Solomon an Inquisitor comes and tests craft users under surveillance to see if they can control their powers. If the craft user is unable to pass the test, they are taken care of.
As witches use their powers against humans for selfish needs usually, Solomon started to hunt them to protect humanity from them. Usually witches are killed by Solomon agents, while only in STN-J are they captured and sent to the Factory alive.
While Craft users can be used to hunt witches, they are surveyed very strictly, so that they will not become destructive.