Gasoline is made in large batches. Each batch has a number of attributes that should be met; Octane, specific chemistry, volatility, contaminates, ethanol content, and others. The output is dependent on the crude that went into the refinery and the processes the refiner has at hand to process it. Refineries vary in there capabilities.
There are over 60 different fuel variations required by government regulation in the US. These are formulated to help with air pollution concerns that vary by region, mostly, but not always due to average weather conditions. Regulators require an average quality across many batches. So that means there are batches that do not meet standard. These are often purchased by low price marketers who then pass on the "savings". Batches are often in the 2 million liter range. Also the brand specific detergent additives are put in at the truck level only in those loads headed for specific retail stations. These additives are expensive and usually not used in the thrift-ed brands.
So yes, there are many differences and the answer is, as is often the case, It Depends!