Not sure about "Regional" but "Reliever" has some specific legalese attached to it, I've heard. Example: KAPA has wording somewhere in some documents (unknown to me) for their Federal monies that they're not supposed to offer "Airline" service... related to their "reliever" status with DEN...
Which makes the Denver Air Connection "charter" stuff (which runs on a schedule)... somewhat of a PITA for the airport management... is what I've heard... but FAA and the airport SO FAR say it's "charter" and not an "airline service"...
http://www.denverairconnection.com/30-seat-dornier
Quite a bit of mumbo-jumbo on their website explaining what "Public Charter" is... and claiming the flights are flown by both Part 135 and Part 121 carriers... carefully not saying which type they are.