v. Buyer will provide written verification of down payment funds in the amount of no less than $XXX,XXX upon signing of LOI. vi. Buyer and seller agree that seller is responsible for the payment of brokerage fees to XYZ Brokerage, Inc. in the amount of $XXX,XXX.
Note that the definitions are not too far apart, but the documents themselves are. The biggest difference is a Purchase Offer is a formal legal document, that once signed by both parties becomes a legal and binding agreement. If you are working with a real estate agent or broker, this is usually the document they will have you sign if you are interested in placing an offer on a property.