I've seen while searching that it is possible to use two different programs on the same computer communicating over the network using the same port and same network interface provided one use UDP and the other TCP. However I didn't get a good explanation, how does it actually work and why this is possible?
Is it also possible for multiple programs to use the same UDP port since UDP does not establish a real connection between the peers, but just sends the packets to an address? I understand it's not possible with TCP as it creates a synchronized connection between the server and the client, but what about UDP?
Please explain in details if possible, or link a good article on the topic.
The other answers are correct but somewhat incomplete.
An IP (aka "INET") socket "connection" (i.e. communication between two processes, possibly on different machines) is defined by a 5-tuple: protocol, source address, source port, destination address, destination port. You can see that this is not limited to a stateful connection such as TCP.
This means that you can bind different processes to any unique instance of that 5-tuple. Because the "protocol" (e.g. TCP and UDP) is part of the differentiating factor, each can have a different process.
Theoretically, you could bind different services to the same TCP port if they bind to different interfaces (network cards, loopback, etc.) though I've never tried it.
It is standard practice, however, to always use the same service on the same port number. If both UDP and TCP are supported, they're just different ways of communicating with that same service. DNS, for example, uses UDP on port 53 for lookup because they are small requests and it's faster than creating a TCP connection but DNS also uses TCP on port 53 for "transfers" which are infrequent and can have large amounts of data.
Lastly, in complete accuracy, it isn't necessarily a 5-tuple. IP uses the "protocol" to pass to the next layer such as TCP and UDP though there are others. TCP and UDP each seperately differentiate connections based on the remaining 4 items. It's possible to create other protocols on top of IP that use completely different (perhaps port-less) differentiation mechanisms.
And then there are different socket "domains", such as the "unix" socket domain, which is completely distinct from "inet" and uses the filesystem for addressing.