When we use SSH, we should have an SSH client on the client computer and there should be an SSH server running on the remote computer. In Linux for example, the SSH daemon, sshd, should be running in the server.
What about in serial connection (RS232)? How does the client computer communicate to the shell of the remote computer? Should there be also a "serial daemon" running on the server?
For historical reasons, Linux treats the serial console the same way it treats the text console when you log on with your monitor and keyboard, which is to say, it's handled by the kernel.
There are processes running in the console. Traditionally there is some variant of getty which is what asks for your username and password, and starts a shell after you do that. That could be considered the main process for the console. However, the console itself is not a process, but something the kernel does.
Using getty is not mandatory; any process (with the needed privileges) can open /dev/ttyS0 and send and receive characters.
