I first came across the term "rainbow draw" quite recently. It refers to the practice of drawing one of each blood tube type from a patient without a clear understanding of which tests are going to be performed. Some tubes have anticoagulants, of which there are there are several types (e.g., heparin, EDTA, citrate), some have serum separator gels, some are just plain tubes and so on. These tubes are recognizable by the different color of their caps and so the allusion to a rainbow. We use different tubes because some assays require serum (e.g., chemistry tests), some require anticoagulated blood (e.g., complete blood counts), some require plasma (e.g., coagulation assays) and so on.
A rainbow draw is a strange approach to sample collection! Some of these tubes are quite specialized, and it's unlikely most patients would routinely need, for example, a tube collected for analysis of heavy metals. I understand that having to re-draw a patient is time consuming and perhaps uncomfortable for the patient, but drawing one of every tube is a waste of tubes, a waste of blood, and a substitute for rational thinking about which tubes are needed for different laboratory tests.