This is a fun month on which to do a birthstone because there seems to be few differences depending on what source is used. However, the majority of sources that I found listed both the Pearl and the Moonstone as being the modern birthstone for June. Of course it could be argued that a pearl is not a stone as such so maybe that's why there are the two.
One thing that both pearls and moonstones have in common is that that while the best known colour for each is probably white, they both can come in several different colours. One thing no one could argue about however is that they are both beautiful stones.
While I don't yet have a piece using moonstone, my moonstone is still sitting in my gemstone collection as yet unused, I do have a couple of pieces made using, amongst other things, pearls. One such piece is my Amethyst and Lampwork Necklace that incorporates a fair few fresh water pearls.
Here are a couple more pieces featuring pearls from members of the JET team:
and here are a couple of pieces using Moonstone: