I mean, would it be possible to a single world to have different historical time periods depending on the location? Like a village/kingdom that have a middle-age-like knowledge and technology, but a city far from there having a modern or futuristic technology, but both in the same time period? Or does if a world advances to another age every place throughout it also advances, with no exceptions?
I see three types of situation in which you may have societies of very different levels of technological advancement surviving at the same time on one world:
- Differential advancement: This is where geographic isolation and differences in the resources and opportunities available to societies mean they develop technological capabilities at different rates. Read Guns, Germs, and Steel by Jared Diamond for several interesting historical case studies of this phenomenon.
- Cultural choice: This is where a society, or those in power in that society, deliberately isolates themselves from other societies and outlaws certain technological advancements. The Japanese period of isolation from the 1630s until 1853 is one example, or the Amish, living 19th century lives in the present-day US, are another.
- Cultural theme park: This is a world in which someone has contrived to create a situation where different cultures at different levels of advancement live side by side. You see this in the story Cathouse in Man-Kzin Wars I or in the Riverworld Series by Philip Jose Farmer.
Differences that result from Differential advancement or Cultural choice always get overcome eventually. There are still uncontacted tribes in the Amazon living essentially stone-age lives, but there is little of the planet that is so remote these days that technological society does not reach it. Europe eventually found the cultures of north and south America with devastating consequences for those cultures. Japan’s isolation was ended when the Americans under Admiral Perry sailed modern war ships into Edo in 1853 and forced Japan to open to outside trade.
If you opt for a natural explanation for why different societies co-exist with radically different levels of technology, you must have a satisfactory reason why the more advanced societies do not enslave or dominate the less advanced societies. Technological advancement reaches a point called the Line of Empire (see Bruce Sterling, Shaping Things), where it’s possible for a more advanced society to dominate less advanced societies militarily, culturally and in terms of trade. The pull of resources and increased living space will mean that a society who can walk over a neighbour is very likely to do so.
This is why authors resort to the Cultural theme park – they must posit an outside power with inscrutable motives that imposes the situation on the world. In the Man-Kzin Wars Cathouse story, there are walls between hexagonal compounds that tile the surface of the planet, each compound contains an environment and a culture from various historical periods and alien races in Larry Niven’s Known Space universe. The mystery of who set up the zoo is central to stories like this.
The worst case of the cultural theme park is the average 1990s Dungeons and Dragons setting, where a Dark Ages Viking society lives next to a high-medieval society or a gun powder using European Renaissance society. No attempt is made to explain why the more-advanced society simply doesn’t stomp their less advanced neighbours and take their stuff.
So the choices seem to be opt for deliberate cultural or geographic isolation, and understand that the differences in development are temporary and some societies will come to dominate others in time, or build yourself a theme park with more or less rationale.
Easily, though out history there are many examples of one civilization been decades and even centuries more technological development then an other. Good examples would be Europe and the American Indians, Pre-industrial Japan and the US, the Mughal and Europe.
Here are some possible explanations for why this might happen.
First post-apocalypse: end of the world happens Society collapses, eventually though people come together and try to rebuild. You could have a scenario one group of survivors is made up of Engineers, scientists, doctors, and other intellectuals. These people would have the knowledge to speed up human technological development as they rebuild Society.
In contrast if their neighboring group of survivors was primarily composed of regular non-intellectual people, then you would have a case where one group was able to rebuild much of the technology we have today in this short amount of time, well the other regressed to a more primitive level of Technology and was unable to reclaim anything close to our current level of Technology for centuries.
Second closed borders: in the early stages of colonization Japan shut its borders forbidding any foreigners save the Dutch from entering Japan on pain of death. This protected Japan from foreign influences but it also closed it off to foreign trade. Because of this Japan missed out on the early stages of the Industrial Revolution, when do United States eventually showed up with its modernize Fleet and demanded that Japan open its borders to trade, it was little the Japanese could do but yield. They knew well enough that swords and arrows cannot stand against modern machine guns. In your world a similar situation might happen with one country closing off its borders to trade and missing out on several technological inventions that are spreading throughout the rest of the world.
Third lack of contact: the American Indians had little contact with Europe or Asia because of the gigantic ocean that separated the old world from the new. Because of this similar to the way Japan missed out on the early stages of industrial Revolution, the American Indians missed out on several inventions that came from Asia to Europe specifically gunpowder. Something similar could happen with your two countries an ocean or a non passable mountain range could prevent contact with one another allowing 1 to develop technologically very quickly and the other to develop much slower.
(Please excuse me if this answer is not what you're looking for; it's my first one.)
An example that might help us understand the situation you are proposing is that of the Inca civilization and the Spanish conquistadors. The Inca were not quite living as one would in your stereotypical (European) middle-aged town, but for our purposes, we can dismiss that in order to draw lines parallel to your scenario. In contrast, the Spanish had developed muskets and war tactics that would send the Inca into disarray during battle. During The Age of Discovery these two contrasting worlds collided, and while the conquistadors were not exactly flying around in F-18s, they were certainly frighteningly much more developed than the indigenous Inca. A display of these technological differences was Battle of Cajamarca, in which the Spanish Conquistadors won by a ridiculous margin.
The biggest (and pretty much only) factor in the separate evolution of technology in these two societies is the large distance in between them, not to mention the (enormous) Atlantic Ocean. So, I would recommend something similar to an ocean in between your two societies.
To tie my point together- yes, it's completely feasible for societies to develop on drastically different technological tracks, but it has to be for a reason (whether that is an unsurpassable mountain range, the stormy terminator of a tidally locked planet or a large body of liquid). In most cases, when there are two towns right next to each other, one of which is chock-full of rockets and robots, and the other brimming with spears and serfs- the people in the latter town are all going to adopt the former town's technology (with the exception of super-strict luddite religions or the like).
I would say there are a few ways that different technological ages would exist, and in fact to some extent they already exist that way.
Geography. There might be no communication between peoples. The higher-technology people can't get to the poorer tech people's place or don't know about them. This is the case before Columbus brought the full invasive force of Europe to them. Perhaps the high-tech people are concerned with space travel, and just have forgotten that any people outside their city even exist. This sort of thing might explain Atlantis.
Economic and cultural reasons. There are places on earth where a few, isolated tribes have stone age technology even now. For some reason we respect their culture and don't try to bring them into the 21st century. Certain places in Mexico are suffering with diseases of malnutrition that haven't been seen elsewhere since Medieval times (Arizona Republic, 2016). For some reason our vaunted generosity has failed to bring succor to them. Maybe the technologically rich take care of their lesser brethren, with deliveries of food and basic medicine but refuse to let the Sleepers learn anything about it or possess any technology.
Superstition, prejudice, war, subjugation. There might be a fear of technology or a refusal to study to learn its secrets on the part of the poor technology people. They might do this for religious reasons, or they might just find schooling somehow degrading. The abundant technologists might feel that their technology is somehow sacred and the others not suited to use it. Perhaps one nation abused the technology, and are forbidden to have anything above medieval level technology or they will be bombed to the stone age. Perhaps the people in one area are 'most dangerous game' and the high-tech people are cannibals or just hunt them for fun. Defensive technology would be forbidden, and any technology is hard to develop while on the run.