All things being equal (for instance, no additives), the hardness number tells you how QUICKLY a cold process soap will saponify and harden up, and how resistant it will be to softening in contact with water. A high hardness number also does usually indicate a soap will end up being pretty hard. All this because the hardness number is derived directly from the amount of saturated oil you use (generally the solid or semi-solid oils).
A lower hardness number indicates a soap that will saponify more slowly. It may still get very hard depending on the oils you use, but it will tend to absorb more water and soften more in active use. Olive oil is a good example of an oil that comes out this way. Trace and ultimate hardening just takes longer.
What really complicates it is the use of non-traditional polyunsaturated oils. These can slow down saponification even more. Certain types and quantities of these oils can make soft soap or even soap that never totally hardens, soap that softens a lot in contact with water, and soap that is much more likely to get rancid.
Paragraph 2 and paragraph 3 can represent very different cases, but Soapcalc doesn't distinguish between them in the hardness number. You have to understand the oils. Basically, a lower hardness number can be okay if you are using liquid oils like olive and not much polyunsaturated oil.