Since this system does not rely on the Internet it is widely used by mariners, RV campers, missionaries, and various agencies who need to communicate when the Internet is not available at the last mile location.
The Winlink system consists of a group of Common Message Servers (CMS) placed at various locations around the world. These servers connect via the Internet to Radio Message Servers (RMS) in many geographic locations to form a star network configuration. The Radio Message Servers are the UHF, VHF, or HF RF gateways into the Winlink system. The final component on either side is a client computing device running the software to send/receive messages through your radio. In Internet terms, you could think of the Radio as a modem (very loosely speaking).
The client computer will generally run Winlink Express if it's a Windows computer, or AirMail if a MacOS (Airmail can also run under WINE or CrossOver on Linux). Yes, Pat and Paclink will run on Linux but it is a bit dismal to try setup and use. Winlink is very skewed towards Windows users which is a great pity.
The client software will also connect via Telnet over the Internet so if your Internet links are up you can use it is in this way. If the Internet is not available your radio would need to establish a connection to a RMS. Here in South Africa, there is a RMS in Cape Town and one in Gauteng so I could manage to connect via VHS radio in Cape Town but if I wanted to try to reach Gauteng's RMS I'd need to go HF (which means it won't be available 24/7 to me). You'd also need to take into account what type of digital mode is supported by the RMS eg. the one in Cape Town is Pactor and VARA so anything else won't connect to it.
A registered user would receive a firstname.lastname@example.org e-mail address for the system. Anyone could then send via the Internet (from Gmail or any other e-mail address) to that e-mail address. A mariner for example at sea would have their radio and computer running and trying to auto-connect say every 10 minutes. In the short period that the radio manages to establish the connection, that mariner would receive waiting e-mails, weather reports, and send any mail they had composed ready for sending. It works in a store-and-forward mode.
It is also possible to make direct peer-to-peer connections between two client computers (radio stations) that are within radio range of each other (could be 30km or 500km). This could also allow a radio station with only VHF/UHF capability to connect to another station with VHF/UHF and the second station could forward the messages into the Winlink system using HF.
If using amateur radio bands the usual restrictions apply and a license is required. But one can see how useful this can be during a disaster as a lot more accurate communication can be exchanged more quickly than during it using phone mode (voice).
There is a lot more detail in the beginner's guide at http://wr4cc.org/wp-content/uploads/2018/01/Beginners-Guide-to-Winlink.pdf