Glucose monitors work on a chemical sample, over which blood is drawn by capillary action. Two electrodes detect the presence of blood by conductance across the sample and the amount of glucose is determined by the change in conductance as the glucose reacts with chemicals in the test area over time. Some meters measure the rate at which the conductance changes ( a differentiator circuit ), others just measures the conductance when it first starts conducting and then again after a set amount of time. They are required to be within 20% and a lab would certify them as accurate if they are within 15% but the technology itself can be within 5% and the variation between test strips of the same batch should be within 2%. Most errors are from usage, they are affected by temperature of the meter, temperature of the test strip, how old the test strip is, humidity, humidity within which the test strip was stored, the amount of time it takes to suck the blood into the test strip, the amount of air the blood has been exposed to, the air currents, what's in the air and the rate at which the blood was drawn from your body ( a slow draw that needed more pushing out has more interstitial fluids then blood ).
It's quite possible that your test strips had been exposed to heat or cold, or that they were not properly sealed since your last use.
An A1C gives you the idea of your average glucose levels by measuring the accumulated exposure to glucose that your blood cells have, you blood cells live for 90-120 days and are produced constantly so the test is representative of the average over 30 to 40 days but it's skewed as it's not a true evenly weighted average so if your glucose levels have not been more or less consistent over the three months, the A1C may not be terribly reliable.
But the varying results are why they require at least two separate FBG tests on separate days or an A1C before diagnosing diabetes.