Aging soap might be a better name, I suppose. But if people confuse saponification with curing -- which in my mind is fairly clear cut -- I can't imagine there will ever be consensus about the gray area when curing stops and aging begins.
There is a good body of research available to scholars and large-scale soap manufacturers that has looked at the various crystalline structures in bar soap; how the crystal structure can be altered by different ways of processing the soap; and how these structures affect the soap properties such as mushing and cracking of the bar, lather volume and quality, smoothness and slickness of the bar in the hand, etc.
It's quite the deal, what little I've been able to dig into it. These findings are another reason why I'm rather skeptical of the "evaporation only" school of thought.