The soap recipe c@lculators I'm aware of only track the main fatty acids found in soap -- lauric, myristic, palmitic, stearic, oleic, linoleic, linolenic, and ricinoleic. If a fat contains significant amounts of fatty acids not tracked by the calc you're using, you'll never know about these "invisible" fatty acids if you simply take the calc results at face value.
For example, the fatty acid profiles for palm kernel oil (PKO) and coconut oil (CO) appear to be about the same in many soap calcs. But there are two "invisible" fatty acids present in these two fats -- capric and caprylic acids.
PKO tends to have lower amounts of capric and caprylic acids. Combined with lauric acid, they will increase the harshness of soap made from CO or PKO. According to my notes, here are typical percentages of the "cleansing" fatty acids in these two fats:
Coconut oil:
Caprylic 8%
Capric 7.5%
Lauric 46%
Myristic 19%
Palm kernel oil:
Caprylic 4%
Capric 4%
Lauric 48%
Myristic 16%
PKO has roughly half the amount of caprylic and capric acids that coconut has. That's very likely the reason why PKO might legitimately be a bit milder to the skin. There could also be some placebo effect going on too, because the lauric acid content in PKO and CO are roughly the same.
Digression: There are other invisible fatty acids. For example, butyric acid, found in dairy milk, isn't tracked by the calcs and it too adds harshness to soap as well as a strong objectionable odor many people don't care for. A tiny amount of butyric in fluid cow's milk isn't enough to increase harshness or add significant odor. But if one makes soap using butter or heavy cream, the larger dose of butyric can be a problem.
edit: And another fat -- fractionated coconut oil (FCO) also called medium chain tryglycerides -- is almost entirely capric and caprylic acids with very little lauric acid and no myristic acid. FCO is nice used as-is for skin and hair care, but makes a very harsh soap. It seems to be a trendy ingredient for new soap makers to use rather than regular coconut, but I sure hope that trend dies out soon.