The human body produces two types of sweat: eccrine and apocrine. Both are odorless in and of themselves. However, when bacteria arrive, they begin to eat the sweat, and the gases they produce emanate from our skin as body odor. Apocrine sweat, which is more oily than eccrine, is produced in areas that aren't normally exposed to air, such as the armpits, groin and feet. Bacteria tend to enjoy feasting on this sweat the most. Unfortunately, the gases they produce are particularly pungent.
So how does soap help us say N-O to B.O.?
Soap molecules have two ends: one that likes to bind with water molecules and one that likes to bond with oil molecules. Because grease gets stubborn in water and refuses to bond with the H2O molecules, it takes soap to act as an intermediary. It does this by surrounding the grease on our bodies with its oil-loving side while bonding to water with its hydrophilic (water-loving) side. This forms an emulsion of grease in water, which can then be washed away. If you'll remember, one of the definitions of a deodorizer is something that can emulsify molecules, which is exactly what soap does.
If sweat is the basis for bacteria to form body odor, and soap removes sweat from our bodies, then it follows that all soap is deodorizing soap. Therefore, deodorizing body washes do in fact remove odors, and don't just cover them up.
So it would seem that "deodorizing" is simply a marketing term that states the obvious (like a moisturizing cream that's touted to fight elbow dryness or a toothpaste that claims it can clean hard-to-reach areas). However, some body washes may contain stronger fragrances than regular soaps. Once they remove the sweat -- and the odor -- from our skin, they leave behind a perfume that could help cover up new odors. If that's your goal, it's best to experiment with a variety of washes to find the one with a fragrance that best suits your skin chemistry and olfactory aesthetics.