Bryan,
You're a bit confused by unfamiliar terminology. Don't worry about it.
You have an "offset smoker." A smoker is also called, a pit, a cooker, and a few other things. There are other kinds of smokers without offsets. For instance "cabinets" and "bullets." Your round type is a "drum," "barrel" or "pipe" smoker. Square types are called "consoles"
Whether console or pipe, all offsets have two chambers. The smaller one is the offset firebox. The larger one is the cooking chamber. Sometimes the firebox is referred to as the offset. Sometimes the cooking chamber is referred to as the cook, smoke or smoking chamber. Even though the smoke is made in the firebox, the smoking (aka barbecuing) is done in the cooking chamber.
Your Maverick Redi-Check is so common in the world of barbecuing that it's also known by its model number, ET-73. When someone says they have a Maverick, they almost always mean an ET-73. If they have an ET-7 or an ET-72, they'll say so. Redi-Check is the name Maverick puts on its entire line of thermometers. No one uses it out loud. Not even Maverick.
Here's some information on the thermometer itself, and how to use it:
The chamber probe is the short, straight probe with the blunt end. It goes along with the little spring clamp. You insert the prongs of the spring clamp between two bars in the cooking grate, then push the probe through the holes. You should measure the smoker's cook chamber temperatures on both sides of where you put your meat, as well as measuirng it as close to the thickets part of the meat.
You do this by putting the probe in an appropriate place to the left of where your meat will eventually go, closing the cook chamber door and giving the cooker enough time for the temperature to stabilize -- at least ten minutes after closing the door. Then measure the temperature to the right of where your meat will go in the same way. If the differential is more than 15 degrees or so, you'll have to rotate the meat occasionally during cooking, or else "tune" your pit to lessen the differential to an acceptable level.
From what you've written, I know you'll want to start on tuning your pit right away. The easiest way to get a good tune on a small offset is with a loaf pan used as a water pan, and a large rectangular pan used as a drip pan. If it's something you're interested in doing, shoot me a line and we'll get into it. Or, start a new thread here and get lots of feedback, some from other Char-Griller owners.
Once you've measured the differential, set your chamber probe where you think it will most accurately reflect the heat of the chamber at the product, and get your meat in there. The "meat" probe goes into the thickest part of the meat -- but you don't want any part of the probe to touch bone, and you don't want the tip, where the sensor is actually located) to land in fat.
Cleaning:
When you clean your thermometer probes, be careful not to submerge the probes and leads in water. If they get wet, they will short out. Guaranteed. Clean the probes and leads with a damp scotch-brite. When cleaning, always hold the probe and lead in such a way so as not to strain the lead where it goes into the probe.
Hope this helps,
Rich