May mom and I used to make soap as a hobby growing up. You make soap through a chemical reaction requiring a diluted lye solution and oil. A properly formulated soap recipe uses more fat than is required for the chemical reaction. you can add significantly more fat for "superfatting" for luxury/ more expensive soaps. Alternatively, you can have just slightly more fat for a margin of error. The reaction that converts raw ingredients into the soap can take days or weeks depending on whether the soap is made using a hot method or cold method.
The type of oil used changes the quality of the soap's foaming action. For instance, castile soap is made with olive oil and produces a specific time of foam. Palm oil makes a "harder" bar of soap helping it last longer. Shea butter makes a soap that has smaller denser foam (almost creamy) and the excess shea butter makes the cleaning process more moisturizing.
There are different legal ways to list ingredients for soap. One is by listing ingredients that were initially added the other is a list of the ingredients present in the final product. Many soap-based products don't list lye because it should no longer be present in the final product.
