Cancellations and delays do have slightly different rules. So the Regulation actually hasn't nothing about delays, that came via court rulings, and that is where the 3 hour rule came from, not the article you quote. There are circumstances where cancellations AND delays can see your payment reduced by half, it depends on the distance. And yes, if the airline gets you to your destination by 2, 3 or 4 hours, depending on distance, then payment terms can vary. So for example if you are on a long flight, a delay between 3 and 4 hours gets 300€ if it is due to delay. If it's due to cancellation and you are 2 hours 45 minutes late it is 300€, if it's due to general delays then you get nothing. I think in time that may be changed, but the courts haven't so far done that.

These sites that offer to do the work for you are a misnomer: you have to provide those websites with the exact same details as say CEDR, the forms may be a little different but you can't avoid some input into the process. CEDR has an automatic process, so they do the chasing. But these sites tend to want to drum up business, and can be non specific when it suits.