Don't feel Stupid WoodLuvr, I'm 53, and have been around Outboard motors and Chainsaws all my life, and your thread is the first that I had heard that there was even a difference, never mind that outboard oil could actually harm a chainsaw.
I don't know if the Old Man, or his cronies ever used outboard oil, it wouldn't surprise me if they did, a lot of our cutting was using boats on the Columbia River, there was/is a Pile wing dam a bit down river from a log dump/rafting site, we used to go scout the wing dam for firewood, tow it back to the moorage, and skid the logs up the boat ramp with our old Ford station wagon to buck them up, we got a LOT of firewood off that wingdam
.
I don't recall having used outboard oil in my own saws, may have happened, not a lot, but it sure won't happen again.
When I was ATVing, we used a Full synthetic, "Golden Spectro", the condition of the P&C's after even a Lot of HARD USE/ABUSE
was incredible, Spectro is Good stuff, but I don't know if it was Liquid/Air Cooled specific, our Honda TRX 250R's were water cooled.
I think that you are in a Very large Club of those who didn't know that there IS a difference, I'm a member of that club myself.
Doug