What exactly is soft soap?

Soft soap is the everyday name used in ordinary speech.

If we want to be more specific and are more knowledgeable about chemistry, soft soap may also be called potassium soap, potassium fatty acid soap, crystal soap, or the potassium salt of fatty acids. Soft soap is usually made from vegetable fats, but it can also be made from animal fats. Making soft soap from animal fat was common in the old rural society, where nothing went to waste. Fat from animals slaughtered in the household was saponified into soft soap for washing themselves and cleaning the house and barn.

Soft soap is used as a cleaning agent, or for assembling pipes or moving/sliding heavier objects on poles. Other traditional uses include combating aphids, foot baths, and treating conditions such as ingrown toenails. Soft soap can be either a thick, jelly-like product packaged in a jar or a block (like butter), or it can be liquid. Its production involves a process in which vegetable or animal fat is boiled together with potassium hydroxide—saponification. This distinguishes soft soap from bar soap, which is made from fat and sodium hydroxide.

You can find superfat and alkaline soft soaps here