I don’t think our two statements are mutually exclusive. There’s certainly a difference between education and being smart.
EDIT: if you disagree, what is someone smart before they get into school? Not smart? In countries where they don’t have formal education systems, is nobody intelligent over there?
Is someone who went to school for 10 years automatically considered smart? That would mean that more school equals more smart. How about somebody who got held back and had to repeat a grade six times? Are they extra smart then? How about those that did so well in school that they skipped a grade? Are they not smart then?
Your logic doesn’t hold up, random disagreeing people. There is absolutely a difference between education and being smart.
There’s not really a way to “source” this until a scientist decides to create a longitudinal study on how people refer to themselves. I’ve never seen one, but maybe one exists. I think this one’s going to have to pretty much remain a personal experience kind of thing for now!