Maybe you're thinking of B Corp? That's just a certification from some group. Public Benefit Corporation, on the other hand, changes directors' fiduciary responsibilities. For example, earlier this year, the Delaware Court of Chancery ruled that PBC directors are not obligated to maximize shareholder value when selling control of their company.
I highly recommend Eric Ries' new book Incorruptible if you want to learn more about this stuff. In there he tells the story of the Vectura Group, a pharma company that was developing treatments for asthma and other respiratory diseases. It was looking at a sale, and it had a couple offers, the one from Phillip Morris slightly edged out the other, and because of fiduciary duty, even though many involved viscerally hated the idea of going to Phillip Morris, as the cause of many of the ailments they sought to cure, they sold to them.