Saponification is the process of "oils becoming soap", to put it simply. We list our ingredients as "saponified oils of..." so that the consumer can see the ingredients more easily. Saponification requires oils/fats and alkali solution (lye and water). All traditional soap is made this way. What about grocery store soap? Yes, they list their ingredients the "INCI" way (chemical composition in short)... Example: Sodium Tallowate is basically saponified tallow (beef fat). Any grocery store soap is probably not handmade and is most likely over processed, but if it has the "Sodium..." elements, it is probably a traditional bar soap, not some strange chemical, like some soap makers would like to suggest. With this said, there are many new detergent type soaps entering the market and many are sold as "handmade". This is unfortunate that "propylene glycol" (one of the main ingredients in these soaps) can be even associated with "natural soaps" but if you look at many melt and pour soaps, it's in there! We've seen a lot of exaggerated claims demonizing the commercial soap industry, but in the end they just make bad soap. In our wonderful nation, with consumer freedom, you can choose not to buy that awful soap, which we feel speaks for itself (no need for exaggerations). So steer clear of bad grocery store soap, and "pseudo handmade soap" (made from propylene glycol and Sodium Lauryl Sulfate) and this will be your best bet.
In short, with the exception of Sodium Lauryl Sulfate (or similar) based liquid soaps, soaps are traditionally made through saponification, if you are buying common beef fat soaps or quality vegetable based handmade soaps.