There is little difference, if you compare CP with HP - both made with potassium hydroxide.
If you're comparing sodium soap to potassium soap - there is an important difference.
Sodium soap is much less "soluble" in water. Which means that it has two phases:
- snot
- soup
Somewhere between the two there is a fine line where the soap is actually useable.
With some downsides:
- it's more diluted and it has less washing power
- it is more prone to bacterial contamination - being more dilluted, it isn't able to stop molds and stuff from growing inside
- has the tendency to clog the soap dispenser, I suspect it also produces more scum, or more dense scum
- sometimes, it separates
The difference in quality is extremely obvious. If you never made potassium soap, you'll be able to guess this difference when comparing your liquid soap to commercial liquid soap. It is possible that certain sodium soap recipes behave better when liquefied, not sure about this.
Even the lye excess for KoH seems weird to me, even if there is an impurity issue, I don't understand why a superfat is a bad thing...
You probably missed my comment in the other thread. Superfat is bad if you are trying to achieve a clear soap, transparent enough to read the newspaper through it.
Many liquid soapers seem to have this goal, which I personally don't understand. Especially that they don't have the same goal for solid soap.