A CEO is often called the Director of the movie.
A CEO has to set high vision and be an evangelist, hires and runs the team, raise money and sets the execution goals bar. While its similar kind of the thing for Product Managers too.
Product Managers are often called the CEO of the product. A product manager has to prepare a vision and set a roadmap for the product.
Product managers needs to be an evangelist with a will to develop at any stage of the product lifecycle and managing the best possible internal team to help and build great products.