Bar oils do actually contain tackifiers. It's one of the reasons why they're the closest substitutes for way lube. While at some level there is probably a difference with a few other additives, In the wide world of lubricants they're much closer to each other than they are apart.
I'm also a believer in any oil is better than no oil. But guys that don't believe in running bar oil, and just use any oil, or used motor oil in their saws because it's just a "waste oil" will see accelerated wear of chains and bars. It just flings off and doesn't stick around like a bar oil would.
I confess that I am shocked.
So much so that I researched your claim and found lots of info to support it.
I didn't find anything to suggest that bar oil was close to or even related to way oil. Just the same, I'd have to accept that they are more alike than different unless someone has info to the contrary.
The reason I am shocked is as follows. With NO EXCEPTIONS, ALL of my current and past chainsaws throw enough oil as to totally overwhelm any need to worry about slinging it. Oil does not accumulate. It flies off in thin streams or mist that goes everywhere. Whatever gets added gets thrown off. The volume is such that I go through two or three 4L jugs of it a year. I always have to add oil when I am out cutting wood. There is so much oil that I often think about figuring out a way to slow it down.
My current saws include an industrial Husky and two 20V Dewalts. I have owned a dozen others in the past including Jonsored, Stihl, & McGarbage. They all piss oil at a rate that I couldn't imagine a sticker adding any value at all.
That's totally different from a lathe or a mill or a surface grinder where the oil has to stay there for a whole working session.
So ya, I'm shocked. Nonetheless, what you say appears to be true. I'm at a total loss to understand why though.
I smell a 50 mile rabbit hole.
Edit - I keep summer and winter bar oil here and use them appropriately.