We discussed this exact topic in the 2010 WSOP supervisor meeting.
Reading through this topic, here are the nuts and bolts of it. "Completing the Bet" is a limit term. "Full bet" is a big bet term. It is Apples vs Oranges. They are not the same even though they are both fruits.
If in No Limit / Pot Limit a player must raise a "Full Bet/Raise" more than the last bet/raise, than equally the betting is reopened to a previous bettor if the total bet to them is a "Full Bet" or more. If the original bettor wishes to raise, they must raise the "Full Bet/Raise" amount more than it is to them.
I think we're all agreeing on this, just in different ways.
What is often confusing is when we say that an all-in bet is not a 'raise' unless it is a "Full Bet". A short all-in bet may not be a 'raise' ("Full Bet"), but it is still action and that action must still be called or raised. If raised, it must raised by the last "Full Bet/Raise".
Also is sometimes confusing differentiating between a "Full Bet" and a "Full Raise". Instead of saying you have to raise a "Full Bet" it is probably more correct to say you to raise a "Full Raise". Most people think you have to raise or double the bet when you say "Full Bet". But when you clarify and say that you have to double the raise or raise the previous raise, they understand better. "Full Bet" is such a universal I'm sure we can redefine it. That's English for you. Where one phrase can mean 5 different things.