When smoking a cigerette, what is the difference when you do that
second inhale (after you have taken the cigerette away from your
mouth)that places all the smoke into the lungs and when you
only do that initial inhale (I think this is what people call "not
inhaling" but I am not completely sure) to take in the smoke from the
cigerette?
Does it only stay in the mouth when you do not do that second inhale? 
I guess you can say I am looking for a comparison reguarding the
effects and simply "where does the smoke go."

When you are taking a drag from a ciggarette, or anything smokable for
that matter, the smoke (for the most part) is going into your mouth,
aka "pulling a Bill Clinton." This is generally only done in cigar
smoking, because when you're smoking a ciggarette you inhale to absorb
the nicotine. Taking the extra breath of oxygen pushes the smoke to
your lungs, and that is when you have inhaled.

Thanks but if it only goes in the mouth is it less harmful to your
body or is there on differnce at all at the amount of "damage" done.

Not inhaling will do no very little, if any lung damage. But it kind
of defeats the purpose people smoke -- to get the nicotine buzz.
Though, overtime smoking (even just in the mouth) can cause mouth
cancer. But overall the risk of getting a disease is way lower.

Many beginning cigarette smokers initially suck the smoke into their
mouths and do not pull it down into their lungs. Gradually, without
even realizing that they are doing it, they tend to start inhaling
more deeply.

It may be possible, but I've never known anyone who maintained a
regular cigarette habit for very long without becoming a deep inhaler.
Although some nicotine (and some carcinogens) will be absorbed through
the lining of the oral cavity, the nicotine "kick" just isn't there
unless you draw the smoke into your lungs.

I smoked my last cigarette in October 1989. I've been inhaling fresh
air ever since, and although it doesn't give me much of a "kick," it
also doesn't give me bad breath, cancer, or heart disease.