There are different approaches one can use to make soap. You can also have a variety of different types of acids to choose from to interact with the base in the soap making process. However there is one rule that all the techniques of soap making follow; regardless of the acid used the base MUST have one ion of hydroxide. It is for this reason that the base of popular choice is lye which as one ion of hydroxide and one ion of sodium. The sodium ion however does not take part in the saponification process. Another base that is used is also potassium hydroxide for the chemical composition of the one ion of hydroxide. Potassium hydroxide is the base of choice that is used in liquid soaps. The acids in soap are fat based. There are many to choose from. Examples are olive oil, coconut oil or tallow. They can be either animal or vegetable based.
Each acid or fat has its own unique composition of triglycerides. Triglycerides are chemical compounds comprised of three fatty molecules attached to a single molecule of glycerol. Every triglyceride reacts with a based differently depending on the type of triglyceride it is. The same is true for the proportions of base to acid used in the soap making process. The amount of base used per soap recipe is contingent upon the chemical composition of the acid. When the correct proportions of base to acid are used saponification occurs. It is the triglyceride in the acid that releases the single glycerol molecule. This molecule then transforms into glycerin when released. The releasing of the glycerol molecule allows the fatty acids to chemically combine with the hydroxide ion to form with the basis into soap.
In conclusion we can say that making soap is composed of two distinct chemical reactions. The first one is when glycerol changes into glycerin. The second is the acid and base chemically interacts to form the soap.