Saponification, and the number behind every recipe
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The reaction the whole craft is built on, and the number that makes a recipe safe or dangerous.
What is actually happening
Fats and oils are triglycerides. An alkali, sodium hydroxide for bars, potassium hydroxide for liquid soap, splits them, producing the alkali salt of the fatty acids, which is soap, and glycerine.
Which is also the legal definition: the bulk of the non-volatile matter being an alkali salt of fatty acids is precisely the output of this reaction.
Once it is complete there is no free lye and no free oil beyond whatever superfat was designed in. Finished soap is not caustic.
The SAP value
Every oil has a saponification value: the amount of alkali needed to saponify a given weight of it.
They differ substantially. Coconut oil needs considerably more sodium hydroxide per gram than olive oil.
Which means you cannot swap one oil for another by weight without recalculating, and this is a consequential fact in the craft.
They also differ between sodium and potassium hydroxide, so a bar recipe is not a liquid soap recipe.
Why a recipe is a calculation
A soap recipe is not a list of quantities. It is a list of oils, each with its SAP value, multiplied out and summed, then reduced by the superfat percentage.
Change any oil, or any quantity, and the lye amount changes.
Which is why every soap maker uses a lye calculator, and why a recipe found on the internet is a starting point rather than an instruction.
Never trust a recipe you did not run
Run any recipe through a calculator before making it, including one from a book and one you made last year from memory.
Check the result is sane: a recipe calling for far more or far less lye than similar ones is telling you something.
And run it again after any substitution, however small. Substituting one oil for another at the same weight without recalculating is how a lye-heavy bar gets made, and a lye-heavy bar burns.