A derrickhand is a member of an oil drilling team that works high above the drilling platform. His primary job function is to help steady the pipes being inserted into the well, to work in conjunction with the driller to ensure the process goes smoothly from start to finish, and to train other drilling team members.
A toolpusher, or "pusher," is the foreman for a drilling crew at an oil rig or other extraction site. As the supervisor on location, the toolpusher is responsible for his drillers, but performs primarily administrative tasks such as ordering and maintaining the proper equipment and materials. However, he likely also has hands-on experience as part of a drilling team himself.