There is a natural shine on this one. I have even seen a "star" shaped shine, I just could not get in any of these photos. It looks like a violet "fancy" sapphire corundrum?
The piece that is polished is absolutely a piece of corundum! And yes they call it star sapphire! nice! The other rock looks to me to be rose quartz. Interestingly enough, rose quartz can also have "optical" properties, when polished in the same way at the corundum, it can have a cats eye shine to it, very much like the star in the corundum!