If I read the OP correctly, I think the context would be different and the question would not be so much the difference between (aerodrome) QNH and QFE, but between aerodrome and area QNH.
The aerodrome QNH and QFE have been answered sufficiently. I would only add that these numbers are updated anytime that that's required, multiple times per hour if necessary.
The area QNH is the lowest QNH that would be predicted over the course of an hour, somewhere in the area concerned. Why the lowest and not an average or the highest predicted? Simply because using the lowest QNH gives the most safety buffer over terrain.
So on any given flight you would use at least three different datums:
- The aerodrome QNH or QFE of the departing aerodrome.
- One or more area QNHs once leaving the immediate vicinity of the departure aerodrome, OR the standard setting of 1013.2 if flying above the TA.
- And lastly the aerodrome QNH or QFE of the destination aerodrome.
Note that normally an area QNH will be the same as, or lower than the aerodrome QNH of an aerodrome in that area. In any case, it can never be higher unless there is a major prediction error.
It is important to understand the differences between all these datums and to understand why they change and may differ from each other, and even calculate one from the other. And then you can even elect to set a different datum than what what is normally required if that suits your style of flying. The NZ example above was very interesting (what do you do if the only "official" QNH is one that's taken 150 nm away?) but I'll give you two more:
We have an annual spot landing competition. As part of this competition, the instructor in the airplane will also look at the neatness and tightness of your circuit, including altitude keeping in the circuit. As the circuit is defined at 700' or 1000' AGL, we set QFE on the altimeter instead of QNH, which is normally used when flying circuits in the Netherlands.
My aerobatics training area is in the Rotterdam TMA which goes from 1500' to FL55. When flying there I keep the altimeter set on the area QNH and read the FL from the transponder. It is very awkward to adjust the altimeter from QNH to 1013 and back every time you spin or loop or zoom through the TA/TL (which is at 3000' over there).