Logging out merely closes all applications being run by the user in question. These could be GUI applications actually seen on screen or background processes. It also, obviously, closes the authenticated computer session, meaning no other user of the computer can sit down at your computer and look at, open, etc. your files.
It's rare that you are ever asked to restart in Mac OS X and even rarer that you are asked to logout. The only example I can think of is when switching video cards on 2008-2009 model MacBook Pros. In that scenario, OS X asks you to logout so it can close all running applications and the display driver itself, switch to the other video card and then come back.
Since, you didn't specify what exact problem you're experience/trying to solve, I can't be of much more help. But, to answer your primary question, no there is no "faster" way to do this because, again, all that's happening is all running processes are being killed. Additionally, you cannot bypass the login window because you have to authenticate yourself in order to access the computer account (files, settings, etc. specific to your user).
The only sidestep would be to enable single user login, where you're essentially telling OS X that you're the only user on the system and it should just go ahead and log you in automatically. But, that creates a bit of a security concern if your computer is ever available to anyone else: for instance, a laptop that you take out of your home.