In
ssh host tail -f file The ssh client connects to the sshd server on host over a TCP connection. sshd runs tail -f with its stdout redirected to a pipe. sshd reads what's coming from the other end of the pipe and encapsulates it in the sshd protocol to send to the ssh client. (with rshd, tail stdout would have been the socket directly, but sshd adds encryption and is able to multiplex several streams (like for port/agent/X11/tunnel redirection, stderr) on a single TCP connection so has to resort to pipes).
When you press CTRL-C, a SIGINT is sent to the ssh client. That causes ssh to die. Upon dying the TCP connection is closed. And therefore, on host, sshd dies as well. tail is not killed, but its stdout is now a pipe with no reader at the other end. So, the next time it writes something to its stdout, it will receive a SIGPIPE and die.
In:
ssh -t host 'tail -f file' It's the same thing except that instead of being with a pipe, the communication between sshd and tail is via a pseudo-terminal. tail's stdout is a slave pseudo-terminal (like /dev/pts/12) and whatever tail write there is read on the master side (possibly modified by the tty line discipline) by sshd and sent encapsulated to the ssh client.
On the client side, with -t, ssh puts the terminal in raw mode. In particular, that disables the terminal canonical mode and terminal signal handling.
So, when you press Ctrl+C, instead of the client's terminal line discipline sending a SIGINT to the ssh job, that just sends the ^C character over the connection to sshd and sshd writes that ^C to the master side of the remote terminal. And the line discipline of the remote terminal sends a SIGINT to tail. tail then dies, and sshd exits and closes the connection and ssh terminates (if it's not otherwise still busy with port forwardings or other).
Also, with -t, if the ssh client dies (for instance if you enter ~.), the connection is closed and sshd dies. As a result, a SIGHUP will be sent to tail.
Now, beware that using -t has side effects. For instance, with the default terminal settings, \n characters are converted to \r\n and more things may happen depending on the remote system, so you may want to issue a stty -opost (to disable output post-processing) on the remote host:
$ ssh localhost 'echo x' | hd 00000000 78 0a |x.| 00000002 $ ssh -t localhost 'echo x' | hd 00000000 78 0d 0a |x..| 00000003 $ ssh -t localhost 'stty -opost; echo x' | hd 00000000 78 0a |x.| 00000002