There’s a number of ways to look at it. I primarily look at it if ILMA’s vs Majors.
A major is typically your vertically integrated oil company. This has gotten a little skewed because of the spin offs and such. But Mobil, Chevron, SOPUS, BP, P66, etc. are all majors. The smallest of which is Citgo (which is also Mystik) - and back in the day, Valvoline when it was Ashland chemical, now it will be again with Motiva.
You also have the odd ducks of ARG (D-A lubricants. As they have a refinery) and KPP (safety kleen). As well as now Vertex who is blending finished product. All those are companies that have refineries, as well as make product.
Your ILMAs are blenders. After all it’s in the name. Pinnacle, Allegheny, Reliance, Warren, Omni, Amalie, etc.
Then you have your contract blenders. Who only produce oil for other people. Also know as toll Blenders.
Gordon Terminal systems for oil, ITS for anti-freeze.
After that you have your brands. And anyone can have a brand if you want to do the paperwork basically.