Adjusted Gross Margin accounts for the cost of maintaining inventory, which regular Gross Margin does not.
Gross margin can be calculated offhand as the selling price of a good minus the price paid for the good (cost of goods sold). This is the simplest calculation for profit. The Adjusted Gross Margin takes into account the cost of maintaining an inventory as well, which is a step in the direction of accounting for the expenses of the business operation as a whole.
Inventory carrying costs include the transportation of inventory, warehousing costs, insurance costs, inventory shrinkage, and opportunity cost. Opportunity cost, in particular, is a fuzzy notion that is decidedly non-GAAP, meaning it is not a Generally Accepted Accounting Principle.