The generally accepted practices are:

A-Stock is, legally, new, unopened product in it's original box. This can mean a box opened for QC and resealed with the QC department's tape before shipment to a dealer or a customer, if selling direct.

Gray Market is a term you may hear and specifically refers to "A Stock" product brought into the US by anyone other than the official manufacturer's importer here in the US. Ex: someone goes to Japan, buys new Sony gear and brings it back to the states to sell it. Sony Corp. of America (the official importer) had nothing to do with the importation.

Yes gray market items may be new (though you have no legal assurance of that) and a fabulous deal, but if they break, the manufacturer is not legally bound to honor the warranty. Neither will an authorized dealer will be willing to repair it -even for a fee. Consider that the manufacturer and the dealer have paid salespeople and advertising costs to promote the brand here in the US. The Gray marketer has done none of that.

Gray market items can be a fabulous value -or a complete disaster.  The items may have been imported illegally, may not have been been properly tested to US standards or may not comply with US regulation. Plus, the manual is probably in Japanese!

A digression: No dealer is legally required to perform warranty work on items they did not sell unless it is required by their contract with the manufacturer. Warranty work is reimbursed by bthe manufacturer at a very low rate and dealers understandably do not wish to lose money on items they did not make a profit on.

Gear becomes B-stock the moment a manufacturer, dealer or designated representatives open the box on a new piece of gear for any other purpose but QC. Legally it cannot be called new anymore. Though B-stock cannot be sold as new, it will almost alwways carry the full warranty as long as it is purchased from an authorized dealer or directly from the manufacturer (this is to maintain a "chain of custody" that ensures the unit was not sold to an end user or is otherwise legally "used"). Sometimes B-stock is new product, but no longer a current model.

Manufacturers or dealers will open a box when they need to demo a product. A manufacturer's rep will carry the product around to dealers or display it at shows. The units typically have low hours and sales reps generally try to keep them in good shape. Authorized dealers may also term items opened for demo as B-stock. Rarely a b-stock item may have had a very minor, usually cosmetic, repair. Manufacturers and dealers are quite rigorous about B-stock status as the consequences for misrepresentation can hurt business and open them to liability.

Bstock cannot come from a third party (i.e. an end user or an unauthorized dealer) unless the manufacturer or authorized dealer have designated that third party (usually a broker like me) to sell it for them. In these cases the warranty will be honored by the manufacturer or the authorized dealer. 

Do not expect deep discounts as the manufacturer and the dealer normally cannot discount the cost on their books. The best time to look for B-stock is at NAB (or other shows) or shortly thereafter. You can often buy gear right off the show floor (though you have to wait for the show to be over!) Do not be afraid to ask at any booth about the possibility of purchasing show gear for a discount. Some folks are clever enough to ask to buy the demo gear before the show! Deep discounts can be had on heavy items as the manufacturer would rather ship it to you than ship it back home.

Refurbs are generally new items that have been returned to the manufacturer under warranty as defective and repaired by the manufacturer or it's officially designated refurbisher. Refurbs often come with a full warranty and can be a good deal; consider that a tech has actually been through the unit and made sure it worked!

C-Stock is a very broad category (with no legal meaning) used for items that a manufacturer or a dealer cannot legally designate as Bstock and generally carry no warranty. They may have been laying around for a while, may be a discontinued model, be beat up cosmetically or possibly are missing parts. C stock may include dealer refurbs (see above for manufacturer refurbs). C stock can carry deep discounts but is generally sold as-is with no presumption that it works, though dealers are pretty careful to let you know what you are getting into.

Used gear is gear that's cannot legally qualify as official A or B stock or was purchased by an end user at any time. Used gear is generally sold as-is unless otherwise stated.

A related question: How do brokers differ from E-Bay? E-bay simply links buyers and sellers and may handle the payment through Pay Pal. The buyer pays the seller and, if the item is trash and the seller will not refund your money, you're SOL. Fat lot of good it does you to slam the guy with a bad rating -that just protects the next guy!

A broker holds the money (escrow) while the seller ships the item. The buyer gets 48 hours to inspect the item after which, if the item is as represented, the seller is paid. If there are issues, the broker mediates a solution -usually a discount for repair but, occasionally, a return and complete refund. Brokers also tend to be knowledgeable about gear and will often give you good advice as to whether a particular piece of used gear is appropriate for your need or is just a bad investment. E-Bay is just a machine!

My site's domain is Bstock.com and at one time I thought I'd be able to list a ton of gear from manufacturers (I was also a manufacturer's rep at the time). The reality is that manufacturers, nowadays, are very careful about keeping b-stock levels as low as possible. So my clever domain name turned out to be a bit of a bomb and that's why the site is branded as Uncle Geo's Greene Sheet!