Merchant
In short
A person or business that sells goods or services to customers and accepts payment for them.
The business behind an offer
A merchant is the seller in a commercial transaction. It might manufacture its own products, resell another brand’s products, or combine both activities. The word describes its selling role, not its size or the software it uses.
In product advertising, separate the product from the offer. Several merchants might sell the same branded item, while each supplies its own price, stock status and delivery information. Matching the product does not make those offers interchangeable.
A marketplace provides a place to trade. Whether the marketplace or a third-party seller is the merchant depends on the transaction. Likewise, a payment processor provides payment services; that alone does not make it the seller.
Illustrative example
Imagine a bicycle shop advertising a helmet manufactured by another company. The manufacturer supplies the brand and product identifier. The shop is the merchant and supplies its own offer details.
If the manufacturer also sells that helmet through its own website, it acts as both brand and merchant for those direct purchases.
Keep the identities separate
Use the actual brand in product attributes and the correct seller in business information. A merchant account for accepting payments and a Google Merchant Center account serve different purposes. Creating either account does not change who manufactured the product.