Which of these is currently active is specified in the mode line. The difference between them is the key-bindings available. All other characters are sent directly to the inferior process, with no interpretation by Emacs. Character mode looks and feels like a real terminal, or a conventional terminal emulator such as xterm. In line mode, key commands mostly have standard Emacs actions.
Regulars characters insert themselves into the buffer.
Line mode is basically the original shell mode from earlier Emacs versions. To switch from line mode to character mode type C-c c . To switch from character mode to line mode type C-c l . Therefor, in line mode after an input line at the end of the buffer is sent to the inferior, it is deleted from the buffer. If you want to login to a remove computer, you can do that just as you would expect, using whatever commands you would normally use.