Much store bought "soap" is not soap at all, but detergent. Detergents are petroleum based products.
A bar of 'SOAP' should say "soap" on the label. Fake soaps can get around the legal issue by calling their products "beauty bars", "moisturising bars" etc. instead.
Look at the long list of ingredients in a commercial "soap" bar - detergents, fillers, chemical preservatives, artificial hardeners. Generally such things are neither kind to your skin nor the environment.
Many commercial soaps have a high animal fat content in the form of sodium tallowate - beef fat combined with lye. It's cheap and plentiful and produces a hard, longlasting bar of soap, but do you really want to rub it on your body?
Glycerin (a highly valued skin moisturiser) is often extracted from commercial soaps and sold on as glycerine - a lucrative by-product - which is then added to higher priced lotions and skin creams. Cold processed handmade soaps retain all their naturally produced glycerin.