DEpends on your definitions
The milk in your fridge that goes bad isn’t just “soured”, though - that’s why it smells rotted. It just spoils first. It doesn’t taste or smell anything like milk that is correctly soured with acidification. I defy you to drink the spoiled milk in your fridge or pour it over your cornbread.
I’m not really familiar with soured milk but this sounds similar to how sour cream is prepared. Commercial sour cream is usually made with heavy cream fermented by lactic acid bacteria, but from what I can see homemade sour cream is generally acidified with lemon juice or vinegar.
Someone once jokingly asked how you can tell that sour cream has gone bad since it’s already sour! The answer of course is that sour cream is a freshly made dairy product, it’s not cream that’s gone bad! It has an expiry date and it’s one of the products where I pay attention to it!