The difference between approved and certified is, or at least should be, that the company is obligated to keep, with a penalty for violating, the standards of the certifying agency.
I would be amazed to hear that any reputable agency would allow its symbol to be used without recourse for violations.
Maybe the shoe comparison has some merit, but the blood pressure medication anology was odd. Obviously, an approval and a certification are doing the same thing – demonstrating the kashrus of a product.