When referred to in the context of piping and plumbing, welding work refers to the task of physically connecting two or more pieces of metal pipe. For some jobs, a pipefitter will lay out the material that needs to be welded, and a separate welder will be responsible for joining the pieces.
Most welders are not specifically plumbing or pipe welders. A welder may be working on a pipe one day and a railing or automobile frame the next. Welders have a specific knowledge of welding, and need have only limited knowledge of plumbing or structural engineering. They're responsible only for their welds and are typically not expected to have familiarity with the project's blueprints.
Pipe fitting encompasses not only the selection of materials and the installation of those materials, but everything in between. Pipe fitting includes the act of fabricating the pipe system to be installed. This includes measuring and laying out the material to be installed. For this reason, pipe fitting is a more in-depth job than just welding, and it requires more specific knowledge.
Pipefitters must be able to read blueprints and have a working knowledge of a wide array of different materials. For some jobs, pipefitters will be responsible for drawing up computer-aided design (CAD) mock-ups of their project prior to beginning any physical work. Typically, pipefitters choose that field specifically as their career, and are neither plumbers nor general contractors.