Yes, you have some terminology mixed up. Saponification is what HP speeds up, thats the process of the oils turning into soap, in CP saponification can take anywhere from a few hours to a couple days.
Cure is completely different, not only does the excess water evaporate making the bar harder but the soap undergoes some chemical changes making it milder and lather better.
HP can actually take longer to cure since its usually made with more water, all that extra water needs additional time to evaporate.
Soap being safe to use and being properly cured are different. HP is safe to use almost immediately but you will end up with a not so great soap that melts away quicker than if it had a good long cure.