The same distinction between "manufacturing" welding and "construction" welding should probably just be applied within all types of welding in general. It's all about the application. Welding just sticks two pieces of metal together, so to use glue as an analogy - it can be used to stick macaroni to paper for a primary school activity, or used during surgery to save someone's life. Same action, two wildly different skill levels required for a successful result.
Having spent some time with prototyping shops and custom product manufacturing houses - those welders are insanely talented. There is an wild amount of knowledge required (metallurgy, chemistry, physics, electronics) to be used in practice, and the physical demands (fine motor control, holding pieces or your body under complete control at various angles/positions) should not be underestimated. Couple that with the understanding of the product being produced and how their actions can improve the end design, and you're left with what I tend to see as the closest thing to a wizard as we have in the modern era.
It's like the old saying goes - "Give a man a hammer and everything starts to look like a nail. Give a man a welder and everything starts looking like whatever the hell he wants it to be."