Softsoaps are liquid/paste-soaps which are made of a type of lye that is Kalium (potassium) hydroxide for short: KOH. The reason for using KOH is because the KOH molecule chain is shorter and gives a more liquid (pasty) soap.
Old fashioned or “pioneer” soaps were made from lye that were made of wood ashes – and were primarily a soft, gooey soap. To harden this soap one could use table salt, which at that time it was expensive.
One can make beautiful shampoo, handswash, floorsoap and more with softsoap. You can use both the castile (olive oil) soap recipe or the coconut soap recipe with KOH instead of NaOH. Notee, you can’t use the same amount of KOH så check the soap calculator. Though the KOH is a bit difficult to find, you’ll get often nice offers on Ebay.com or sometimes drain-cleaners can be a 50% KOH so they work!
Here is an nice recipe with pictures.
This is in a diluted form.