There are two types of test.
1. Blood plasma test, which is a test which measures the glucose in your blood plasma at that point in time, ie a snapshot and
2. HBA1c test, which is the amount of gycated haemoglobin in your blood. This is very different to a plasma test and is a record of the past 3 months.
Many tests at the doctors are plasma tests. As you mention 11.3, it sounds more like a plasma test but, ask the doctor.
The difference between you doing a test with a meter and strip at home is that you are using capillary blood from a finger prick. At the doctors, they use a needle and take a sample of venous blood, ie from your vein, and this is much more accurate. The capillary contains other fluids and so is not as accurate as blood from a vein. They both test the level of glucose in the plasma, but the doctor's reading is likely more accurate.