...Does using mango butter make any difference or give any extra in terms of quality and scent after saponification is complete ? For instance, can we understand the difference between Palm-Coconut-Olive soap and Mango-Coconut-Olive soap ? Can we just say ''Yes, it's so obvious that this soap was made of mango butter'' ?
I think you have to keep in mind that the fats used to make soap don't remain fats after saponification is done. The only exception is the fat that remains as superfat and (a) superfat is only a small portion of the soap that mostly goes down the drain when bathing and (b) it's likely the superfat is never 100% the original intact fat after the lye gets done reacting fully, so any residual mango butter probably isn't fully mango butter anymore.
Saponification breaks down the fats into fatty acids and those FAs are turned into the soap. The properties of soap are far more similar to the properties of the FAs, not of the fats.
In the end, however, you have to do your own testing to determine whether you think an expensive or unusual fat adds enough benefit to be worth using in your soap. I'd say newer soapers are more caught up in the idea of using exotic fats in soap for their purported luxury benefits, but as one gets more experience, experience tends to prove otherwise. And if you get into selling, the extra expense also argues against using costly fats.
One reason why experienced soap makers might use nut butters in their soap is if they're trying to avoid animal fats (lard, tallow), soy (hydrogenated soy, aka soy wax), and palm oil. All these fats are rich sources of palmitic and stearic acids that add physical hardness and lower water solubility to the soap. The net effect of having a moderate amount of these FAs in soap is that they increase the longevity and mildness of the soap.
The secondary reason why the nut butters are used is "label appeal." My friend Renae taught me how to make soap; she always put 10% shea in her batches. I started making soap with her shea-based recipe, but eventually eliminated shea in my favorite recipe. After trying my mostly-lard soaps, Renae realized the soap was just as nice as her shea-based recipe.
The scent provided by fats is insignificant -- even those who say they can smell the scent of unrefined cocoa butter in soap, for example, never say it's a strong, lasting scent. Same goes for the fragrance provided by infused oils, teas, etc. There simply isn't enough of the scent in these ingredients to add a lasting, definite fragrance in soap.
Essential oils (EOs) and fragrance oils (FOs) are a LOT more concentrated, so they are considerably more likely to scent soap well enough to please most people. And some EOs and FOs still don't work well. And they all tend to fade over time.