Branded gasoline has the company name of the refinery that produced it. Gas stations that are branded like Shell, Mobil, BP, etc. use a product that is refined and delivered to their own same brand stations.
Unbranded gasoline is refined fuel products that are sold at gas stations in convenience stores, and other locations.
Branded Gasoline is the company developed and sold gasoline usually at their own stations.
A great analogy that explains this is the use of “no-name brands” in supermarkets. These brands are perfectly fine and in many cases, they are produced by the same company that makes the branded form of the product.
Again back to gasoline. The product sold to convenience store stations may be a different blend than the name brand uses but it comes from the same refinery.