docker run/exec -i will connect the STDIN of the command inside the container to the STDIN of the docker run/exec itself.
    So

    • docker run -i alpine cat gives you an empty line waiting for input. Type “hello” you get an echo “hello”. The container will not exit until you send CTRL+D because the main process cat is waiting for input from the infinite stream that is the terminal input of the docker run.
    • On the other hand echo "hello" | docker run -i alpine cat will print “hello” and exit immediately because cat notices that the input stream has ended and terminates itself.

    If you try docker ps after you exit either of the above, you will not find any running containers. In both cases, cat itself has terminated, thus docker has terminated the container.

    Now for “-t”, this tells the main process inside docker that its input is a terminal device.
    So

    • docker run -t alpine cat will give you an empty line, but if you try to type “hello”, you will not get any echo. This is because while cat is connected to a terminal input, this input is not connected to your input. The “hello” that you typed did not reach the input of cat. cat is waiting for input that never arrives.
    • echo "hello" | docker run -t alpine cat will also give you an empty line and will not exit the container on CTRL-D but you will not get an echo “hello” because you didn’t pass -i

    If you send CTRL+C, you get your shell back, but if you try docker ps now, you see the cat container still running. This is because cat is still waiting on an input stream that was never closed. I have not found any useful use for the -t alone without being combined with -i.

    Now, for -it together. This tells cat that its input is a terminal and in the same time connect this terminal to the input of docker run which is a terminal. docker run/exec will make sure that its own input is in fact a tty before passing it to cat. This is why you will get a input device is not a TTY if you try echo "hello" | docker run -it alpine cat because in this case, the input of docker run itself is the pipe from the previous echo and not the terminal where docker run is executed
    Finally, why would you need to pass -t if -i will do the trick of connecting your input to cat‘s input? This is because commands treat the input differently if it’s a terminal. This is also best illustrated by example

    • docker run -e MYSQL_ROOT_PASSWORD=123 -i mariadb mysql -u root -p will give you a password prompt. If you type the password, the characters are printed visibly.
    • docker run -i alpine sh will give you an empty line. If you type a command like ls you get an output, but you will not get a prompt or colored output( https://www.mkssoftware.com/docs/man1/ls.1.asp ).

    In the last two cases, you get this behavior because mysql as well as shell were not treating the input as a tty and thus did not use tty specific behavior like masking the input or coloring the output.