A terminal is a physical device for access to a computer. The VT-100 and Teletype ADM-33 are both examples. Xterm is a
terminal emulator for X--it pretends to be something like a VT-220, so you can run your text mode programs.
TTY, of course, stands for Teletype, which was a common terminal used in the early days of Unix. In the old days, you'd talk about having a whole room full of TTYs. Now, it seems to refer to the emulated terminals provided by a Unix-like system.
A console would originally be a specific terminal (often hard-copy, like a Teletype) hooked directly to the computer for administrative tasks.