A Crock-Pot is a slow cooker. But a slow cooker is not necessarily a Crock-Pot. Oh no.
Crock-Pot® (with hyphenation, capitalization, and trademark thingy, please) is the brand name of a line of slow cookers manufactured and sold under the Rival® brand name, which, in turn, is owned by the Holmes Group of Milford, Mass. The term slow cooker is the generic product name for a stand-alone appliance with a heating element and ceramic casserole dish that cooks foods with slow, moist heat.
If one of Rival's rivals (Sunbeam, Hamilton Beach, Farberware, etc.) were to refer to one of their products as a Crock-Pot, you can bet Rival's lawyers would be all over them in an instant, arguing trademark infringement. But the world's recipe writers, working as they do with delicious ingredients that have multiple names, and classical techniques that have developed over hundreds of years, and precious pots and pans that were passed down from their favorite great aunts - who are concerned only with taste and presentation and cookbook sales - can't be bothered by such mundane considerations as trademarks and corporate legal departments. So they write "slow cooker" or "crockpot" or "crock pot" or "crock-pot," and leave it to their editors (who should be concerned with trademarks and corporate lawyers) to fix it.
Rival faces the same problem that all companies do in protecting their trademarks, just as Kimberly-Clark does with Kleenex® tissues and Parker Brothers (now owned by Hasbro) did with its Monopoly® real-estate trading game. In many cases, the trademarked name is so commonly used as the generic product name that the public is confused, and occasionally - as in the case of Monopoly - a judge will rule that the trademarked name has become so general that the company can no longer claim to own the name. Now, you wouldn't want to see that happen with Crock-Pot®, would you?
Although the folks at Rival might not agree, from a cook's point of view, there is no difference in general between Crock-Pot® slow cookers and other brands of slow cookers.