As the oil differs, what is available for blending and cutting is different. There are certain types of molecules in regular and mid-grade BASE gasolines that simply do not exist in premium gasoline that cause much of this. What you buy is additized gasoline. However, you'll see them called additives in many places by many people. Blending components are part of base gasoline.
Oil companies swap base gasoline all the time.
Let's say I have a refinery in Houston and you have one in Dallas. It makes little sense for me to truck my Houston gasoline to Dallas and for you to truck your gasoline from Dallas to Houston when gasoline is a commodity product. So, I let you draw 100,000 gallons of base gasoline from my storage tank in Houston for your Houston gas stations, and you let me draw 100,000 gallons of base gasoline from your Dallas holding tanks for my Dallas gas stations. That way, we both save on shipping. Yup, Texaco gasoline may have come from a Shell refinery and vice-versa.