Hi meche,
A non-diabetic person will usually have a blood sugar around 5 most of the day, and it's normally quite close to that (i.e. it varies up and down a little bit but not a lot). However, at certain times of day it goes a bit lower or a bit higher, and as ever it varies a little bit from person to person. So there's also a "normal range" defined, which is between 4 and 7, and readings within that range are usually considered normal. It sounds like this might be the reason for the two conflicting messages you've had (one referred to the top of the "normal range", the other referred to the "average" reading most non-diabetics have).
I know it's hard when you're waiting for blood results, but I'd try not to worry unduly until you get the results and can see your doctor to discuss them.