Try it sometime... If you use Pam or other spray oil, there are usually soy or other additives that leave a sticky shell on your pan. If you want to experiment on your own, buy a new, cheap pan and fry up some eggs 4-5 times.
You'll see a brown residue on the sides of the pan -- that the stuff.
The brown residue is most likely oil that's partially burned on (or partially polymerized to use the article's term). You can get this residue from any fat. You're just more likely to see it with spray oils because the spray is not precise so you get overspray in undesired areas.
No, that's different. Cooking sprays usually include Soy lecithin, which can cook on (if you don't wash it off) and forms a sticky brown residue. The polymerized oil is slippery.
The residue issue is more pronounced in thick/dark pans like cast iron that retain heat for a long time -- unless you clean them immediately, the residue cooks on. If you cook some eggs, eat, and go back to clean your cast-iron pan, the oil will have been cooked on.
The solution for this use case is to use something like the "Misto", which is a spray pump that lets you spray plain oil on a pan.
If you're not cleaning off the overspray, you'll definitely get sticky brown residue from oil. Oil is only slippery after it's fully polymerized. If it's partially polymerized, it's a sticky mess. Oil on the sides of the pan will generally not fully polymerize without a cycle in the oven because there isn't enough heat being applied.
You'll see a brown residue on the sides of the pan -- that the stuff.