A lot of commercial soap manufacturers (not all of them though) remove the glycerin that is produced during the saponification process and add synthetic lathering agents (commonly used ones are sulfates surfactants), synthetic fragrance, and artificial colors. Most of these ingredients are potentially harmful to our body because your skin will absorb whatever comes in contact with them, and these chemicals might also be toxic to our nature. Plenty of synthetic ingredients from soap, body washes, shampoos, and other beauty products were and are still sneaking their way through the filters at water purification plants. These products usually don't carry the name of "soap" because they didn't include lye in the ingredients. They often market it as "solid shower gel" or "beauty bar".
A natural soap bar would be using pure animal or vegetable oils (or fats), pure essential oils as a fragrance, and natural colorants. Different oils (or fats) have a different composition of fatty acid and provide different properties to a bar soap as well as different benefits to our skin. For example, shea butter is extremely nourishing and moisturizing due to its high percentage of oleic acid, at the same time high percentage of stearic acid in shea butter makes a harder bar soap that would last longer. Just remember, when you choose a natural bar soap, the ingredients are usually extremely eco-friendly and super sweet to your skin as well.
Hope you enjoy the GLOW!