Sourdough is a blanket term that covers any baked goods raised with a sourdough starter.. Many people have an almost instinctive identification of a specific bread as "sourdough bread".
It could be a San Francisco Sourdough Bread, a French Levain bread, a German Rye Bread, or many other breads. And that is the point here. From about 6,500 BCE until 1850 AD, almost all breads were made with sourdough.
When someone wants a "real sourdough" chances are they are identifying the bread of their memories as the one true sourdough. It's fine to want the bread of your youth, the bread of your ancestors, and to feel homesick until you again taste that taste.
But as bakers we should recognize that there's a lot of great sourdough breads in the world. I try to embrace them all, but some are, to my taste, better than others. And that's OK too.