Probably all soap makers at one point wondered if palm oil and palm kernel oil were similar. I know I did...
As has been suggested, oils and fats used in soap making vary in their fatty acid makeup.
It is largely this fatty acid variation that explains the variation in finished soap properties.
If you go to
http://www.soapcalc.net/calc/SoapCalcWP.asp or some other
soap calculator, you can see the fatty acid variation.
On the left side of the calculator, look for the fatty acid make-up of the various oils.
As you toggle from coconut oil to palm kernel oil, you will note that the fatty acid composition is very similar. Compare that to olive oil. See how different it is?
Now if you look at palm oil and compare it to lard, you'll again see how similar they are...
And so forth...
If you spend some time looking at the different oils in the calculator it will quickly show you how the oil compositions vary. Again, that oil variation largely explains variation in finished soap properties.
I could waste hours just looking at the fat variations... Actually I guess I already have over the years...
Then you could stand around in the oil aisle at the store reading labels...