It does make a difference.
Many mom-and-pop places and a few places with low prices manage it by having sub-par storage tanks. To get an idea of what sort of effect his can have on your engine, grab a funnel and pour about half a cup of water into your gas tank, along with a pinch or two of dirt and/or rust. Many times I have filed up at such a place, my car didn’t run right until I burned that tank and refilled it. A couple of times, I had to get my tank pumped it was so bad.
As for those that say premium gas doesn’t matter, that depends on the car. Most non-turbocharged cars built since 1995 run just fine on 87 octane. THose with turbos or superchargers, as well as some “sport” models with high compression engines may require better gas to avoid severe engine damage, but those are uncommon.
Older (pre-OBDII) cars are different though, especially those with distributors instead of solid-state ignotion. Many of the cars I’ve had ran better on Premium and were actually cheaper to run since the increased $/gallon was more than offset by the increased MPG. And both AE82 Corollas I’ve owned (my first car and my current one) made/make hellacious rattling noises and lost/lose enough power to not be able to exceed 50MPH on level ground or to climb a hill with a tank of 87-octane, so Premium is pretty much required.