There are at least 5 "schools" but of course they are growing and blending all the time. Pipes started out as a factory thing, you have a template of things like billiards and bulldogs, shapes that take to being machined out. There is always lots of "hand work" on any pipe but the idea on these pipes is that in a sense, they all come out the same.
In the 60s, some crazy Danes got the idea that maybe pipes didn't have to be so boring, and starting making shapes that were unique, and more than that, shapes where the grain of the wood was not just a random circumstance. Sixten Ivarsson is probably the first guy that people look at in this regard. But this blossoms into an aesthetic school where curves are very careful and mathematical, shapes are often sparse (certain ones like the Blowfish have become more complicated) and even severe at times.
If you contrast this with Japanese pipes, for example, you see a huge difference in proportions and goals.... Japanese pipes feature little nods to nature, assymetry, more mixed finishes, additions of traditional decorations - generally it's really easy to tell a Japanese pipe from a Danish one, and sometimes the easiest way to learn about this stuff is to go look at a hundred examples. Look at Tokutomi and Satau for examples.
There may be an American school at this point, where ideas from the other schools are understood and applied, but the shaping is a little more traditional. Rad Davis and Ryan Alden would be good examples, as would Roush and Butera I guess. Myself too if I think about it, having been taught mostly by Americans, I have embraced most of those ideas, even if I mostly make factory-ish shapes now. Airway construction, internal setup is paramount in this school too, where some of those old Danish pipes are pretty poor inside (again corrected, these schools affect each other).
I'll stick the Italain neo-classicism in here - you see pipes that are almost parodies of the traditional factory pipes - ballooned out, elongated, squashed. Playful shapes. Fun pipes. But far less care in terms of those exacting Danish curves, right, like... close enough will usually do on these. The very best examples are indeed very well and carefully made pipes. The difficulty everyone else seems to have in making a Castello 55 shape properly is proof.
Look again at Russian pipes - lots of crazy shaping, a little more organic than Danish ones but less than Japanese - almost a mechanized them in some of them, like if you drew a cartoon of an animal, made it a robot, and then made it a pipe... lots of little details and shapes, anything goes as long as it's interesting. Yashtylov and Revyagin are great examples.
