Soap has been around since 2800 BC in Ancient Babylon. That is pretty old, and the actual process hasn't changed much since then. The chemistry of soap is fairly simple add lye (originally alkaline salts and tree ash) water with oils let emulsify with lots of stirring and then let it set, cut, store to let it cure for anywhere from 4 weeks to over a year depending on the type of oils used.
Soap oils originally were primarily animal fat - lard. In the 7th century, Arabic people started using vegetable oils in place of the lard - yes, our first Vegan soap. In addition, they infused the oils with herbs for scents and also used colorants. I imagine that most of the soaps looked similar to our handmade soaps today. Animal fats have been used throughout history and are still used is soap making today.
Around 1200 AD, France, Italy, and Spain became the larger producers of soap, each one with their own 'recipe'. The began adding more perfumes and such to their soaps depending on its use - bathing, shaving, laundry, etc.
Through the 1700's and 1800's soap processing changed into the beginning of commercial process and the first powdered soaps became available.
In 1916, Germany developed synthetic detergents which began the trend towards what we call 'soap' in your store today. The production also changed and Proctor and Gamble developed a 'continuous process' which meant you could get soap in a day.
So, why choose a handmade bar of soap to one processed. The process used removes all the glycerin from the soap - they use it in lotions. So, now you need to have lotion because the soap is drying to your skin. Commercial soaps also will blend filler ingredients and chemicals such as Sodium Isethionate (a foam enhancer) and Dipropylene Glycol (a chemical solvent). Handmade soap makers know how to work with their recipes (combinations of oils, milks of various sorts, honey/sugars) to bring a variety of qualities to their soaps.
To answer that question you are probably wondering about - Lye - it is very dangerous. Yes it is. and we take great care when making it to ensure safety. The good thing to know is that, once the bar reaches you, the lye is totally gone - it is used as a catalyst and is necessary to make soap. This is why you will not see it on a label - you will see the word saponified followed by an oil name either in the common or scientific.
The best way for YOU to know the difference in a commercial bar compared to handmade, is to try a bar of handmade soap. Read the label to be sure the ingredients fit into your values for something you want to put on your skin or family's.