Yes, this can get confusing and let me tell you that even experienced pros debate this stuff as they often take different paths to learning it.
The first thing to know is that you have your everyday drummers that study and incorporate rudiments into their playing. Then you have "corp" and/or "orchestra" specific drummers that have a more traditional approach to rudiments. They incorporate more press rolls into their rudiments.
Now to get to your question (or the answer): They're both right. First off, you must know that "closed" has two different meanings. One is to simply play it sped up, where it starts sounding seamless and where RR or LL is played literally. The second is to play the double stroke as a buzz stroke. So instead of having "R R" played in one hand, you will play "zzz" (or buzz) where the stick "presses" into the head. This comes from the "press" roll technique or "buzz stroke" technique.
Example: You can play a 5 stroke roll two different ways. On is like this: RRLLR LLRRL (played literally). The other we can use the same notation above but you will buzz each RR and LL stroke. So you get "buzz buzz R, buzz buzz L"
I advise to study the differences between the double stroke roll and the press roll. This will help when it comes to understanding all the other rudiments that incorporate the doubles.
I could very well be confusing you even more but I hope I've shed some light on it. If you plan to play mostly drumset, I would stick with the literal stickings like on drumrudiments.com. If you plan to get into corp drumming or do orchestra or symphonic work, you might want to lean more toward the approach on the PAS site. Of course it's also OK to learn both. Most pro drummers are comfortable with both.
Good luck and welcome to Drum Chat!
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