"tty" is an abbreviation for "Teletype". The first terminals were Teletypes (like remotely controlled typewriters). See subsection Teletypes. A list of Linux devices (the stuff in the /dev directory) may be found in "Linux Allocated Devices" which should be included with kernel sources. It "describes" what each device used for in only a word or two but doesn't tell you how to use them.
The computer considers each serial port to be a "device". It's sometimes called a terminal device since at one time terminals were the common use for the serial port. For each such serial port there is a special file in the /dev (device) directory. /dev/ttyS0 is the special file for the serial port known as COM1 in the DOS/Windows world. To send text to a terminal you may redirect standard output of some command-line command to the appropriate special file. For example typing "echo test > /dev/ttyS1" at the command prompt should send the word "test" to the terminal on ttyS1 (COM2) provided you have write permission on /dev/ttyS1. Similarly, typing "cat my_file > /dev/ttyS0" will send the contents of the file my_file to COM1 (ttyS0).
In addition to ttyS0 (/dev/ttyS0), ttyS1, ttyS2, etc. (the "S" stands for Serial port) there is also a "cua" series: cua0, cua1, cua2, etc. cua0 is the same port as ttyS0, etc. The "cu" of cua stands for CalloUt. The ttyS series are Posix compliant while using cua may permit the opening of a port that the modem control lines say is not ready. Starting with kernel version 2.2 cua is obsolete and a warning message is issued when you attempt to use it (although it still works). For the past few years it has only been included with Linux for backwards compatibility. A programmer can arrange things so that ttyS can behave just like cua, so cua is not really needed.
Pseudo terminals are pairs of devices such as /dev/ptyp3 and /dev/ttyp3. There is no physical device directly associated with either of them, not even a serial port connector. But if a program treats ttyp3 like it was a serial port, what is read and written to that port appears on the other member of the pair (ptyp3) which another program uses to read and write to. Thus two programs talk to each other via this method and one program (on ttyp3) thinks it's talking to a serial port.
You can't just take a pair of programs and make them talk to each other this way without modifying the source C code. Thus it's mainly programmers that must concern themselves with pseudo terminals and most users don't worry about them.
For example, if someone connects via telnet to your computer over a network, they may wind up connected to the device /dev/ptyp2 (a pseudo terminal port). The login process logs them in to /dev/ttyp2. Here the login program and the telnet program talk to each other via a "pseudo terminal". In X Window, the terminal emulator program, xterm (or rxvt), uses pseudo terminals. Ham radio programs under Linux also use them. Using certain application software it is possible to have 2 or more pseudo terminals attached to the same physical serial port.
For a pseudo terminal pair such as ptyp3 and ttyp3, the pty... is the master or controlling terminal and the tty... is the slave. There are only 16 ttyp's: ttyp0-ttypf (f is a hexadecimal digit). To get more pairs, the 3 letters q, r, s may be used instead of p. For example the pair ttys8, ptys8 is a pseudo terminal pair. The master and slave are really the same "port" but the slave is used by the application program and the master is used by a network program (or the like) which supplies (and gets) data to/from the slave port.
Unix98 doesn't use the above but instead uses a "pty master" which is /dev/ptmx. This can supply a pty on demand. While other unix-like systems have a manual page for pseudo terminals (may be named "pty") Linux lacks one. A page devoted to only to pseudo terminals is needed for Linux. There is both a Linux pty module and a /usr/include/pty.h file.
/dev/tty stands for the controlling terminal (if any) for the current process. To find out which tty's are attached to which processes use the "ps -a" command at the shell prompt (command line). Look at the "tty" column. For the shell process you're in, /dev/tty is the terminal you are now using. Type "tty" at the shell prompt to see what it is (see manual pg. tty(1)). /dev/tty is something like a link to the actually terminal device name with some additional features for C-programmers: see the manual page tty(4).
N stands for an integer. One use of these in Linux is with the ISDN driver package: isdn4linux. The ttyIN is something like ttySN. There is also a cuiN which is something like cuaN. The ttyI and cui emulate modems and may be given modem commands.
In Linux the PC monitor is usually called the console and has several device special files associated with it: tty0, tty1, tty2, etc. When you log in you are on tty1. To go to tty2 (on the same screen) press down the 2 keys Alt(left)-F3. For tty3 use Left Alt-F3, etc. These (tty1, tty2, tty3, etc.) are called "virtual terminals". tty0 is just an alias for the current virtual terminal and it's where messages from the system are sent. Thus messages from the system will be seen on the console (monitor) regardless of which virtual terminal it is displaying.
You may log in to different virtual terminals and thus have a few different sessions with the computer going on at the same time. Only the system or the root user may write to /dev/tty0 to which /dev/console is sometimes linked. For more info on the console see The Linux Console.
The /dev directory comes supplied with many device special files. If you need something that's not there you may try to create it with the "mknod" command. See the manual page ttys(4) for how to do this for serial ports. To use mknod you must know the major and minor device numbers. You might be able to infer the numbers you need by using the "ls -l" command in the /dev directory. It will display the major and minor numbers of existing special files.