Is there a difference between a carpentry meter stick and a clinical height mete!

One of them could be telling lies.
The one that conforms to SI units is the one to believe (Systems International).
Then again you could be making wrongful readings, test by try measuring the two rulers together to see whether the cm units scribed are in fact equal.
Bare in mind there is no such thing as a totally accurate measurement.

Proof take a simple ruler and measure a cm mark it with a pencil, add to that measurement another cm, continue to do this one cm at a time until you have done twenty in total, I will guarantee that you will not have an overall measurement of twenty cm when you have finished, this is because no measurement can be precise it is always a case of we are nearly there , WHICH is why the system international was needed to define how accurate we need to be in differing forms of everyday life. I.E. engineers need greater accuracy than school children drawing triangles and space technicians need a higher degree of accuracy to be certain their plans to land spacecraft on distant planets will actually succeed.

There shhould be no difference in the units used. An inch is fairly well established as to its size.The pattern for the standards of weights and measures establish what the dimensions of the units we use to measure everything. Chemicals, mass standards for weight related technologies like scales, and measurement standards for linear or distance measurement called gages. A gage as near to a perfect centimeter is used to set the equipment for manufacturing the tools originally.
In the US our national standards are mostly kept by government agencies primarily the National Institute for Standards and Technology in Maryland. All secondary and field standards must be compared to a high tolerance standard periodically and that must be compared against another up the line all the way to the international standards kept in Europe. In a low temperature vault in France is the international kilogram for example and it io made from platinum that is almost pure and kept in a frozen state to keep it as stable as possible . The process of comparing standards is called "Traceability".

So technically speaking a centimeter is a centimeter and that is controlled and established as to its dimension. After saying that I should inform that a measuring instrument is only as good as the quality of the place that manufactured it and different levels of tolerance are applied to medicine and aerospace technology than those required for carpentry. The best explanation I can give you for the difference is that the clinical measuring device is designed to measure human beings and the construction yardstick is not. The units are standard but the tool designed for the job is likely better suited to give accuracy in that task and the one to go by

Calibration of laboratory instruments is part of my job. I work in the pharmaceutical industry where a high level of scrutiny is placed on all instruments used in the manufacture of drugs and drug materials. Detailed records of standards used for calibration of equipment and kept ready for inspection by the FDA. I have worked with hundreds of different traceable standards and supervised their maintenance and certification as well. The science is called Metrology. Th9;he science of measurement.