Since we've had a couple of questions about this, just a quick rundown on how stocking influences the pieces you get:

Logosmas stockings yield the lowest number of pieces and tend to be less valuable (you can still roll big pieces on these, they're just less common than higher tiers).
Fancy are basically better logosmas ones. Higher chance at more pieces, better pieces come up more often.
Grand stockings roll more pieces and if you roll low end pieces will roll additional ones to compensate. They also have a flat chance to guarantee a high end piece, but best to consider those a bonus when they come up given that its not a sure thing.
Extravagant stockings guarantee you two high end pieces no matter what, and roll you more pieces after those are awarded.

High end pieces will be pieces from the 1000 credits and up value talismans.

Hopefully that should clear up most questions!

Penned by My hand on the 3rd of Glacian, in the year 874 AF.