Luke is having some trouble logging in.
Here is an address of the item he is asking about
They have a 30 day return policy, so you can order one and send it back if you don't like it.
A true gem quality necklace will have fantastic luster of the highest quality. Luster includes not only "mirror", the reflective shininess, but "orient", the play of colors reflecting from the nacre. The factor of luster that is most rare is "water". Water is a translucency of the upper layers. If you get a gem quality CFWP strand, all of of the individual pearls should display excellent mirror. Most of the individual pearls should display orient and you will be lucky to get some pearls that have much water.
Without having actual examples of two different sellers' pearls to compare in person, it is impossible to tell what they mean by their grading scales.
My guess with the amount of info I have, is that pearl source's AAAA is similar to PP's AAA. Let us know what you think.
I think the true gem quality pearls are set aside for earrings before the rest of pearls are sorted into the usual grades. I do know that that Jeremy of Pearl Paradise started buying the loose earring pearls and having them matched for necklaces resulting in his gem quality.