HbA1c stands for "Haemoglobin Ac1" so is exactly the same as Ac1, its just an abbreviation.
There is no need to fast for a HbA1c/A1c.
The only test you will normally have to fast for is a cholesterol "full lipid panel" test as any fat eaten in the hours before a test will skew the results as digested fat is quite normally carried through the bloodstream as cholesterol.
The paragraphs below in italics and between quotation marks are taken from medical sources, they are not my own assumptions.
Haemoglobin.
"About 90% of hemoglobin is hemoglobin A. (The "A" stands for adult type.) Although one chemical component accounts for 92% of hemoglobin A, approximately 8% of hemoglobin A is made up of minor components that are chemically slightly different. These minor components include hemoglobin A1c, A1b, A1a1, and A1a2."
Fats.
"Lipase enzymes break down fat into fatty acids and glycerol. Digestion of fat in the small intestine is helped by bile, made in the liver. Bile breaks the fat into small droplets that are easier for the lipase enzymes to work on.
Most lipids that you consume in your diet are fats. Some digestion occurs in your mouth and the stomach, but most takes place in the small intestine. Bile is produced by your liver, stored and released in your gall bladder and emulsifies fat globules into smaller droplets".
Cholesterol.
"Cholesterol is a fat (also called a lipid) that your body needs to work properly. Too much bad cholesterol can increase your chance of getting heart disease, stroke, and other problems. The medical term for high blood cholesterol is lipid disorder, hyperlipidemia, or hypercholesterolemia".
