Meaning 1. Neat soap in classic soapmaking terms is a physical phase (like solid, liquid, and gas phase) during soap making in which the soap has a uniform, flowable jelly-like consistency. The neat-soap phase depends on a combination of the fatty acids, temperature, and moisture content of the soap mixture. When people cook soap to a "vaseline" consistency or their soap has "gelled", what they mean is their soap was in a neat soap phase.
Meaning 2. "Neat" in other contexts means 100% pure. Like sometimes people will use an essential oil "neat" meaning they are using the EO undiluted.
I don't know how you could predict a neat soap-phase (meaning 1) in a soap calculator, so I can only think the calc is using "neat" to mean the percentage of 100% pure soap in the batch (meaning 2). This would be calculated by adding up the the weight of the soap (lye + fats) and dividing that answer by the total batch weight (lye + fats + water). Looking at several of my recipes, the % of pure soap in the recipes is around 77% give or take a bit. So I suspect the calc is using "neat" in the sense of Meaning 2.
ETA: Just read what calc you're talking about. Yeah, summerbee is set up for a type of liquid soap making in which you need to know the "paste weight" in order to figure out how much water to add to dilute the soap. That's "neat soap" in the sense of Meaning 2.