The world of wires is more complicated than it might seem.
Wires of one kind or another are a critical part of our everyday life, from those that bring electricity into homes and businesses to those that do the same thing with data to and from computers and printers. In the latter case, many are being replaced with wireless technology so the familiar physical wire is not required. And, of course, we cannot forget cell phones and similar devices.
Not to be outdone, appliance makers of things like electric kettles and power tools often promote the same idea but really mean there is no wire between the business end of the device and its primary power source. But their power sources are all wired up so they are technically not wireless at all. You just don’t have a power cord trailing behind the device when you’re using it.
In metrology, wires are still used—and will be for a long time—when high accuracy measurements are required. The reason for this is because the specifications for threads all call for pitch diameter measurements to be made using wires of a specified diameter under a specified measuring force. There are other areas that use the same concept such as gears and splines. 
Since pitch diameter is unseen, wires of a specified size are used so they will contact the thread at the appropriate position and a measurement is made over them. Pitch diameter measurements in North America are made with a set of three wires that are of a specified diameter and roundness, and the requirement for commonality. This means that the wires in a set may be within their diameter tolerance but the diameters must match each other within a specified amount. 
Some off-shore thread wires are provided in holders, enabling them to be clipped onto micrometer anvils, which makes handling them easy. But their tolerances—and often their nominal dimensions—are to European standards that do not match those used in North America. They can be used for threaded product measurement in many cases, but not for gage calibration.
There are also sets of thread wires—usually six or more pitches—in a plastic pouch that appear to be made to North American specs and they are, except for their accuracy, which is often equal to that of the feature they are being used to measure. While cheap, they are not suitable for anything other than maintenance work.
Many users of thread measuring wires are not familiar with some of these requirements and, while they may have properly made wires, inaccuracies creep into their work. One of the causes of this is a failure to recognize that only the central one inch or 25 millimeters of the wire length has to meet the published standards. I regularly see measurements for pitch diameter being made over wires sticking out from the threads where the critical portion of the wire is not in contact with the work. 
It is assumed that wires are straight but where the small diameter wires used for the finer threads are involved, it is not uncommon to find them bent, which will introduce errors.
Some calculations are required when using thread wires to determine the “over wire” dimension that the usual measuring device will provide. Often this “constant” factor has been calculated by their maker and is shown on a bit of paper that comes with them. This is another area where errors are generated in the measurement process. Often this bit of paper is lost and textbooks or standards are consulted for this “constant” dimension. As you have no doubt suspected, there’s a problem in doing this.
The “constant” is computed based on the actual wire diameter, not the theoretical “best wire” size shown in these tables. To use such generic numbers can introduce significant errors in the measurement. 
You should make sure that any laboratory that calibrates your wires will provide an updated “constant” based on their calibration of them. If they are unable to do so, their calibration work may be a bit dicey so you’d be better off using a laboratory that is experienced in this area. 
It’s amazing how some shiny bits of wire can be so complicated when they look so simple.