If the plaintiff appeals, then, during and notwithstanding the pendency of such appeal, the plaintiff is entitled to enforce, or accept from the defendant or from any person claiming under him or her, performance of all obligations imposed upon such defendant by the terms of any lease, contract, covenant or agreement under which the defendant claims the right to possession, or by law, as if such appeal has not been taken, without thereby affecting the appeal or the judgment appealed from, and without thereby creating or reinstating any tenancy or other relationship of the parties. However, if the result of the prosecution of such appeal and entry of final judgment is that the defendant was obligated to the plaintiff during the pendency thereof in a different form, manner or amount than that in which any payment or payments made under the provision of this Section was or were enforced or accepted, or in a different form, manner or amount than that adjudged in any judgment entered by any court in any other proceedings instituted by virtue of the provisions of this Section during the pendency of the appeal, such payment or payments shall be deemed to have been made to apply in the form, manner and amount resulting or arising from the prosecution of such appeal, on account of the defendant’s obligation.