Private label products refers to product labels that are owned by the selling company and not owned by the producer or manufacturer. Sometimes a well known label, like ConAgra and Sara Lee, will produce secondary products, such as those sold under the name Great Value exclusively for the Walmart stores, that become private labels owned by the seller and not by the producer, in this example, not owned by ConAgra and Sara Lee. Most often though, a producer may have an exclusively "private label" business that provides goods to a variety of store-owned private labels, like the "generic" private labels on goods at Vons and Safeway or Shaws and Albertsons.
Designer brands are produced by a known, named designer who has a signature or a logo on their specialty, usually high-end products. Examples are Calvin Klein, Jimmy Choo, Coach, Coco Channel and Vera Wang. Most often, designer label brands refers to products in the apparel and apparel accessories markets. In contrast, the Sara Lee and Colonel Sanders and Denison's label brands are product brands that are not "designer" but are exclusive brands. Wolfgang Puck might represent a designer label brand in food products, as might Paul Newman.