Your information is not complete.
I would start with
How Soap Is Made (commercially), then take a read through the
Colgate-Palmolive Patent.
To save a little bit of time, the first commercial (manufacturing) processing of soap was done via the Kettle Method and patented by Heilsberg & Co G M B H 1936-38: Fats and Alkali are melted in a "kettle" (steel tank that is three stories high and hold several thousand pounds of material). Steam coils within the tank, heat the mixture. The mixture then gets salted (with real salt) to separate the soap and glycerin. The soap rises to the top, the glycerin settles to the bottom and is removed. More alkali is added to make sure no fats are left unsaponified. Then 'pitching' occurs...the soap is boiled again and water added as to separate the soap into two layers. The top layer is called "neat soap" which is 70% soap and 30% water; the bottom layer is called "nigre" and it contains most of the impurities (dirt, salt and the rest of the water that was added). The soap then gets poured into molds, where it is cooled, cut into bars, wrapped and aged.
The Continuous Process Method was patented by the Colgate Palmolive Peet Co 1942-45. It starts with a big steel column with two drains low on the side of the tank. Molten fat in pour into the top, water at 266F/130C comes from the bottom, pressured is introduced and the fats separate into 'fatty acids' and 'glycerin' and pumped out. It's called 'continuous' because it doesn't stop...as the separated components are pumped out, fat and water are pumped in. The fatty acids are then purified and mixed with alkali to form 'soap'. Added ingredients like abrasives and fragrance are also added and the hot liquid soap is then whipped to incorporate air. The soap then gets poured into molds and then put into a special freezer to harden. The soap then gets 'milled'. Logs of soap are feed through a 'noodler' then sent to a mill. The mill is a set of heavy rollers that crush and kneed the soap. As sheets of soap come off the mill, it goes through another press that forms the soap into logs, the logs are cut into bars, the bars then get put into another press that stamps the name of the company and produces many of the shapes we see today. The soap then gets wrapped and aged.
The above is pretty simplified and doesn't sound too much different than what a Hot Process soap maker would do...except separating out the glycerin for additional profitability and milling the soap. But commercial soap makers needed to get their soap to market a lot faster...and cheaper. The patent describes various experiments tried with different fats (coconut oil, palm oil, palm kernel oil, cottonseed oil, tallow, menhaden oil, olive oil, corn oil, tung oil, soya bean oil, whale oil, etc.) and adding various phosphates before or after the glycerin was removed, trying different techniques and then aging the soap between two and three months.
A lot has changed in commercial soap making over the last 80 years. The majority of the soap on the market isn't even 'soap'...it's why you will see "bath bar", "beauty bar" or if it is supposed to be a liquid soap, it's labeled as "shower gel" or "body wash"...they are more closely related to the detergent you wash your clothes or dishes with and far removed from the soaps that you or I make.
And so yes...because they aren't making real soap, they can dump their ingredients into a pot and produce a product in short amount of time.
It was so funny last night. My husband, before I started making soap, lived and breathed Tropical Dial. So last night he asked me if I have any Peach or Cantaloupe Soap in stock. I told him that I wasn't sure, but when daughter and I were cleaning out from under the sink cabinets, I found 8 bars of Tropical Dial he could use. He snarled at me and said "yuck". Then made a happy, kissy-kissy face when I returned from the garage with two bars of Peach.