Shabegger, the "confusion" stems from the recent change in rules, and I think there are some webpages that have not yet been updated... Now you MUST have PCCs from each State. (I'm told this is because the FBI does not have legal access to State databases, altho states can access the FBI's...)
I am a US citizen, have lived abroad and currently live in Canada, which is (these days) considered "abroad." (How times have changed...).
US Embassies represent the federal government, they may be able to assist with information or the FBI check, but not the states. MAY do fingerprints, may have FBI fingerprint cards, DEPENDS where you are and which Embassy is in your jurisdiction. They all have websites...
Yes, it is a royal PITA - expensive, time-consuming, and made all the worse if you live outside the US.
I had to do 7, some accepted personal checks (I still have a US bank account), some required USD money orders (expensive) - I had to make myself a tracking form to keep everything straight

, some required fingerprints, some on the FBI card, some on their own that you have to order in advance - YIKES.
State fingerprint requirements are more strict than the FBI, I have not seen one that accepted anything but their own form or the FBI's. For most, you have to order the card from them, increasing processing time. Note that the info on the FBI site applies ONLY to the FBI check, has nothing to do with the states.
NC LOOKs awful, but it actually turned out to be the easiest because: they provide an email address and will respond to requests via email... Of the 7 states, NC was the ONLY one I could communicate with by email, so to me that makes them the best. And, once I sent the fingerprint card, it was processed immediately - was the fastest

But it WAS a pain because of the strict process for taking fingerprints (my fingerprinter was just rolling her eyes...)