Firstly they are not modes but just tags to make it easier to reference previous readings. They do not do anything different in terms of the actual test performed.
For example you might want to compare today's fasting readings with those from a week ago, it will be easier to look through ones tagged as AC rather than having to remember what time you ate a week ago to find it based on the time.
As for the readings, they are within the normal margins of error for any meter. And your levels will be constantly changing as your blood is flowing, so one reading to the next will be slightly different.
It is better to treat your levels as being more general rather than to the fraction, so a 5.6 or 6.3 can both be considered as being "around 6".
Of course, a 5.6 could also be considered "around 5" if combined with a reading of 4.8. But that level of details is rarely important, you just need to have a general idea of whether you are too low, too high, or roughly whereabout in between. All you need is an impression of what your body is doing or how it is reacting, you cannot manage it to the fractions.