Once we get into the true Middle Ages, the history of pottery in Europe, especially for wealthy patrons, often became the quest for porcelain, and was always a search for more colour. When Chinese pottery was traded into the West, it amazed European potters and consumers. It was pure white, highly coloured, extremely strong yet incredibly light. Sometimes you could even see light through it.
Potters today have the advantages of science to tell them what's happening with clay and glazes (and even that doesn't always appease the kiln gods, as all potters know!). They had to rely on tradition and experience to tell them what their local clay could and could not do. Culture and tradition, passed from one generation to the next, told potters how to build a kiln, how to fire it, how to know when it was finished. Until science explained the physics, chemistry and mechanics of firing, European potters could not have known that they could never achieve the same results with European clay that Chinese potters could with Chinese clay.
The Chinese pots were made of porcelain and stoneware, which must be fired to much hotter temperatures than earthenware. All European clay, with a few exceptions, is earthenware. Earthenware has some advantages over stoneware: it's easier to work with, easier to fire, and doesn't shrink or deform as much. From an economic standpoint, it's also good because it breaks easily, so the potter is kept busy making more pottery to replace the broken stuff.
But it's thick and can be difficult to shape into any fine detail. Most of the naturally occurring clays fire brown, red, or grey, sometimes cream. And I should add that there are deposits of stoneware clay in Germany, so there has been a tradition of salt-glazed stoneware there for centuries, but it's a local phenomenon, not part of the overall development of European pottery.
As the Middle Ages wore on, potters tried a number of ways of imitating the decoration of porcelain. Tin glazes are one method: a thick glaze containing tin is put onto the pot, then decorated with mineral colours. This gives you a nice white background to work on, but it's still just not the same as porcelain.
Sgraffito was another way. The white clays of Europe don't make good pottery. But if you paint a thin layer of white over red clay, it gives you that desirable white surface to decorate. Now you can colour it and glaze it, or you can scratch through it and make a pattern using the darker clay underneath.
It wasn't until the eighteenth century that European potters found a way of making European clay almost as thin as porcelain. They mixed bone with fine white clay to get bone china. However, bone china will never be translucent like some fine porcelain.
In the twentieth century, the aesthetic of Asian pottery took over the world of ceramic artists in North America. Asian pottery is exquisite. The clay allows the potter to make very fine, thin pots with infinitely fine details of carving and finishing. And the glazes glow like jewels. The kiln technology has to be highly developed, because it can take weeks to load and fire a kiln to reach the temperatures needed for the clay. This means that every kiln load is a huge investment of time, materials, fuel and effort for the potters, so it pays to take the time to make each pot as close to perfect as possible.
Whereas the technique and aesthetic of European pottery is that of the Dixie cup. Easy to make, easy to fire (just dig a pit in the ground!), easy to break, easily replaced. Court records from Staffordshire show that it was not uncommon for English potters to dig up sections of roadway for the clay, which was, understandably, frowned upon by the authorities.
A point I should make is that clay is very heavy, so potters are stuck using the clay near their home. Some ceramic materials, such as lead, colouring agents or clays used for decoration, may be traded over a distance, but for most of human history, pottery was literally home-made. This means that an area with no clay suitable for making pottery will not develop a pottery tradition. It would take generations to learn how to make the best use of the local clays, where deposits were and what different types might be suited to. And tradition is a strong force. If your ancestors never did slip-trailing, then even if you migrate to a locale that has wonderful clay for making decorative slips, it will never occur to you to use clay this way. Potters guard their secrets like cooks and wine-makers, and pottery was not a highly developed or organized craft the way other crafts have been, partly because the skills that work in one location may not work in the next county.
The aesthetic of much European pottery, but especially that of the Italian Renaissance, is exactly the obverse of the aesthetic of Oriental pottery. Oriental pottery, as we have all been taught as good little potters, values the form of the pot as the main consideration. The decoration only serves to enhance the form of the pot. Pottery must have "good bones."
While some early pottery (the beakers of the Beaker People in Britain, Anglo-Saxon urns) have clearly defined strong shapes, the aesthetic is not as refined as in Asia. Some medieval pottery is downright ugly, partly because the glaze technology was not very good but partly because the clay wasn't good enough to hold a shape, or the potters had no models to work from to show them how to make a beautiful pot that is both elegant and strong. The Italian Renaissance ideal was that the pot is a vehicle for the decoration. This makes earthenware in general, and medieval European pottery in particular, difficult for modern potters to appreciate. We have been taught since the time of Bernard Leach in the 1920s and later, that the only decent pottery is Japanese and Chinese (Korean is pretty good, too), while European pottery is a sad second cousin. I certainly was given no appreciation at all for earthenware, and had to re-educate myself. Ironically, Leach himself studied medieval European pottery and did a lot to replicate historical techniques like slip-trailing, but that aspect of his career doesn't always get conveyed to art students in North America.
This is starting to change. More pottery is being made by artist potters that includes vivid colour and decoration
The immediacy of earthenware pottery can create a charm and personality that some of the refined and elegant Asian pottery lacks. European earthenware was quickly made for a local market. The potters often knew the purchasers and users of their pottery well, so they might add a grinning face for cousin Betty on this jug, and make that one in the shape of a ram for Uncle Herbert, who is proud of his sheep. This was not high art. It wasn't destined to grace the tables of nobility. This was destined for the kitchens and pantries of people in the village or the manor where the potter worked. Especially in earlier pottery, there is a freedom of expression that isn't seen in more refined artforms. As late as Tudor times, there is a quirkiness and humour in British medieval pottery. Jugs and mugs have faces, salt cellars are in the shape of ladies or animals.
The kilns were easy to build and easy to fire, relatively speaking, so a load of pottery wasn't a big investment. Make a few pots, fire them, they break, make some more.
If you watch potters in Mexico at work, there is a similar sense. It's dirty work, and often back-breaking. But they crank out pots at an amazing rate, fire once a week or so, and get quick results. There's a lack of attachment to each pot that frees up the flow of ideas. If you're making a hundred of something, you can't afford to get bound in detail. And you might as well have some fun!