There is no inherent difference between Rival and Crock-Pot slow cookers because Rival is the original manufacturer of the Crock-Pot brand slow cooker. Today, the Crock-Pot brand offers more models and options than the Rival brand.
Slow cookers have come to be popularly referred to as crock-pots, but Crock-Pot is a specific brand that Rival developed in the 1970s. Slow cookers work by submerging a cooking "crock" in another vessel that contains a heating element. The crock warms slowly and remains warm, thereby slowly cooking food over a significant length of time. This ultimately provides safe cooking when away from home, and can provide cooking results that faster stovetop or in-oven methods lack. The Crock-Pot brand is still a highly popular slow cooker brand and offers a multitude of slow cooking options at a variety of prices.
Crock-Pot brand slow cookers are available from Amazon.com, Wal-Mart or from Crock-Pot's own website. Slow cookers offer many potential options. A recent Crock-Pot innovation is a programmable slow cooker that allows the cook to choose a protein and a time he would like it to be done. Slow cookers also come in an array of sizes, styles and designs, including portable lunch warmer models.