Call it cheap petrol, call it supermarket petrol. Everyone knows it's cheaper and millions of motorists fill up at non-premium stations every day without giving a second thought to why the petrol is cheaper. The normal excuse is "it's all the same isn't it?". I'll tell you why it's not.
A friend of mine is a petrol delivery driver for one of our local refineries. They subcontract with four well known brands (Texaco, Chevron, Phillips66 and Exxon or Esso) as well as two budget chains.
First of all, he has two different trailers. If he's delivering to the premium outlets he uses one trailer. The budget outlets use another. For the four big chains, the process is essentially the same. The truck is filled with 3 loads of 3,000 gallons of petrol (3 tanks for the three octane levels) then stops at the additive pump for the relevant chain and add in a measured amount of their additive package to each tank (eg. Techron for Chevron and Texaco). The additive package is mixed during the delivery purely by the motion of the truck and the resulting pumpout. The tanks are dumped into the underground storage tanks at the petrol station, then he goes back to get another load. Rinse and repeat.
For the budget chains, things are slightly different. He has to use the other trailer and fills that up from a different delivery pump at the refinery. No stop at the additive pumps - straight to the retailer to fill their underground tanks. In the bottom of that trailer, from weeks of delivery work, there's a layer of sand, silt, grit - something particulate - lining the bottom of the tanks. With the dipstick, he can poke a measurable hole in the particulate, like poking your finger in wet sand.
Essentially, when oil is turned into petrol, it's distilled and filtered a great many times to create the final product. Cheap supermarket/budget petrol misses out one last step of filtration and refining. That's why it's cheap. The grade and quality isn't as high, and it has the potential for more particulates held in suspension. It shifts the responsibility to the owners of the petrol stations to ensure their pump filters are kept clean and in good working order. Cutting that last step at the refinery means cheaper bulk prices to the petrol station, which is why they can undercut the major chains. In the area where I live, this is especially important to know because one of the sources of our oil is oil shale, an organic-rich fine-grained sedimentary rock.
Now does the last step in refining make any difference to your car's ability to use it? Absolutely not - it's gravy. But it's the gravy that's required for the blend of additive package to work correctly for the big chains. They create those additives dependent on fully refined petrol. And because it goes through one more filtration process, the larger chains can be guaranteed of a cleaner end product with less particulate in suspension, which translates to a reduced risk of filter problems on the forecourt.
So there you go. It's not "all the same" - not by any stretch of the imagination. Pay your money and make your choice.