Here is the easiest way to differentiate between a real factory warranty, a factory extended warranty, and all the variations of service contracts/insurance policies, etc. that the marketing folks call extended warranties.
If you paid for it, it is not a factory warranty or a factory extended warranty. It is a service contract.
And here's what a real factory extended warranty is. Consider the case of the original Twin Cam engines back in 1999-2000, where there were early cam bearing failures. The management of Harley decided to extend the coverage beyond the standard warranty for a period of 5 years or 50,000 miles if I remember correctly. This did not cost the customer anything. I saw a lot of this in the auto industry over the years, where we would extend coverage automatically on things that had higher than normal failure rates even though the issue didn't qualify for a recall. It provided customer assistance at a lower cost than a full blown recall, since we only repaired the X% that actually failed.
Harley-Davidson is paid by the service contract folks for the use of their name and trademark, and the dealer is paid a profit when you buy that service contract. The rest of the money goes to the insurance company or other entity that actually administers the program, and it covers repair costs as well as administrative costs plus a profit. So all the folks who buy these plans are the ones paying collectively for the repairs, not H-D or the dealer. It's just like other insurance products in that regard.
Read the actual contract rather than just listen to a salesman. They are allowed to call those plans whatever they want for marketing purposes, but when you get to the legal contracts you will find that they are required to spell it out a little more clearly. And they often have different rules and restrictions than the real factory warranty.
Jerry