Lapis Lazuli is a relatively soft type of gemstone which can be carved into a variety of shapes. What makes this particular gemstone unique is that Lapis Lazuli's color is a deep night-sky blue, but the gemstones are always flecked with small fool's-gold (pyrite) traces which gives the gem the appearance of a night sky dotted with golden stars.
This gemstone's fame comes mostly from its mysticism and it's decidedly "feminine" gearing. As gemstones go, it's actual worth isn't very high, but it remains popular nonetheless. Moonstones are opaque, white-silver stones that under moonlight appear exactly the same shade as the moon in the sky. Naturally, this feature is what gave rise to its historic popularity.
When people refer to jade, they often mean nephrite. This material is a bright opaque green, and its physical quality compared to another form of jade, jadeite, is softer and more malleable. Large pieces of nephrite are easier to find than jadeite, and aside from jewelry this gemstone occurs naturally in pieces large enough to carve into small figurines and statues. Smaller pieces are carved into entire pieces of jewelry like bracelets and brooches.
Opal Jewellery are completely opaque quartz crystals which, like chalcedony, display a multitude of colors at the same time. The biggest difference between the two is that chalcedony's color patterns are often set parallel to each other, and chalcedony stones themselves are semi transparent. Opal jewellery are completely opaque, and the splash of colors is random and haphazard throughout the surface of the gem.