Natural soap is made the same as 2000 years ago- no difference. Commercial "natural soap" is just named so because of marketing reasons.
To make a natural or traditional soap you need fats, some water and lye solution / caustic soda. When you join all of them in the right proportions and at the right temperature, you will initialise saponification process. The temperature determinates if this process will take some hours (hot process) or many weeks (cold process). I use usually a cold process, so I need to be patient.
After that time the caustic soda turns into salt- sodium of specific oil and it is not present in a soap itself. Every oil has its own qualities and is either more cleansing or more moisturising. A combination of different oils gives us a product of expected desires. Soaps can be also pampered with essential oils, dry and fresh herbs, clays, seeds etc. I don’t ever give any artificial colour or fragrance to my soaps.
Natural soaps are perfect to keep the skin and scalp in good condition. They are naturally hypoallergenic- minimalising the potential allergic reaction. Although natural soaps are alkali- they don’t ruin the natural ph of the skin (an argument for producer of artificial cleansers), they last long, don’t require plastic containers or fancy packaging and they are produced from sustainable sources. Natural soap water solution is good for fighting some garden pests.
If you love and appreciate hand made products, you will enjoy natural soap.