Inner 440 Beltline, Outer 440 Beltline. It looks clear enough on a Raleigh highway map, but it can be confusing when you have to pick the right on-ramp in the thick of traffic.
DOT is making plans to simply the circuit ("Redesigned Beltline signs to drop 'Inner' and 'Outer'"). New signs will eliminate the need to think clockwise / counterclockwise. Now wherever you are, you'll be on east or west I-40 (southern Beltline), or on east or west I-440 (the rest).
Better? Do you have trouble finding your way around the Beltline and Raleigh? Let me know.