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GAH refers to the Gold Auction House, where items are sold with gold as the currency. This is as opposed to the RMAH or Real Money Auction House, where players pay for gear with actual currency.

As currency can be used to purchase gold, which can then be used in the GAH, the line between the two auctions houses is blurred and the prices generally work out equivalently, once you factor in the fees and transfer costs. (The exception is at the very high end, since RMAH item sales are capped at $250. That works out to about 1 billion gold at the minimum gold price of 1m gold for $0.25, while top items sell for up to 2 billion gold in the GAH.)

There is no RMAH for Hardcore, and the RMAH is legally-prohibited in some regions (such as Korea). In those markets, the only supported Auction House currency is gold, though of course black market sites exist to fill that gap in legally-provided gold sales.