First, I want to add a bit more to my previous answer about why stearic acid and fats high in stearic are not the same. We were talking at that point about using stearic acid as a supercream ingredient. When used as a thickener, the stearic acid doesn't go through any chemical reaction. It's just a mechanical thickener -- a lot like stirring dirt into a bucket of water. Add enough dirt to the water, and you get thick mud, but the dirt doesn't change its chemical nature.
"...why does the stearic component of shea, tallow, etc go towards the thick, creamy lather of a soap when not used as a supercream?..."
When turned into soap, the stearic acid, no matter whether it's from shea butter or stearic acid pellets, goes through a chemical reaction so it is no longer shea butter or stearic acid. The product you have is the SOAPS that come from shea or stearic acid.
Saponification (1) breaks down fats into fatty acids and glycerin and (2) turns the fatty acids into soap.
You can saponify stearic acid directly, as when we do when making cream soap (see Lindy's recipe in this thread) or make shave soap (see Songwind's "my first shave soap is a success" thread). A lot of commercial soaps are made by direct saponification of various fatty acids.
Or you can use stearic acid indirectly by using a fat that is high in this FA. Shea is mostly stearic and oleic fatty acids with a dab of palmitic and linoleic acids. So when you turn shea into soap, you end up with stearic soap + oleic soap + a touch of palmitic soap + a touch of linoleic soap + the unsaponifiable ingredients in shea. The soap isn't exactly a "shea soap" -- it's the soap that is made from the fatty acids in the shea.
Any soap made with a high percentage of stearic (or palmitic) acid tends to have a low amount of creamy lather, so you're going to see this type of lather with any fat or fatty acid blend high in palmitic and stearic.
Why, you wonder?
Stearic and palmitic soaps are not very soluble in water, so they don't rub off easily onto your washcloth compared to, say, the soaps from coconut oil. Less soap on your washcloth => less lather. These soaps are also rather long, heavy molecules, so they don't fluff up easily into a big puffy lather, compared with soap that comes from coconut oil which contains lighter, shorter, and more water soluble soap molecules.
I hope this answers your question.