A "STAR" flight is the first-flight of the day for an aircraft departing before 0900. Getting the first flight of an aircraft out on-time has been shown to increase the likelihood that the plane will remain on schedule the rest of the day not counting any uncontrollable circumstances such as weather, ATC delays or maintenance issues.
A "PRIORITY" flight is one that may have numerous passenger connections or may have a very tight ground time when doing a turn or through-flight at an outstation which could impact the down-line schedule of the aircraft, connections, crew duty.