Except as provided in this section for an action under § 6–308 of this subtitle, any person aggrieved by a final decision of the Board in a contested case, as defined in the Administrative Procedure Act, may petition for judicial review as allowed by the Administrative Procedure Act. Any person aggrieved by a final decision of the Board under § 6–308 of this subtitle may not appeal to the Secretary but may take a direct judicial appeal as provided in the Administrative Procedure Act. The Board may grant a stay of enforcement of a Board order in accordance with the Administrative Procedure Act. An order by the Board may not be stayed pending judicial review. The Board may appeal a decision that reverses or modifies its order.