In a DUI case, the crime lab will typically first test the blood for alcohol even when there is no suspicion of alcohol. If the results reflect a BAC above a 0.08 then typically no further testing will be done--though depending on the court and crime lab I have seen a further drug screen done even after blood tests positive for alcohol (especially for City of Phoenix cases).
If the BAC is less than a 0.08 and there is some suspicion of drugs, then a drug screen will typically be done to detect the positive presence of any one of various classes of drugs. Some drugs are harder to detect in the blood than others. However, the screen typically includes the illegal drugs commonly thought of as well as many prescription-only drugs. If the screen is positive for any of the categories of drugs then further testing will be done to try and accurately identify the drug in the blood.