Tensile testing is performed on a test coupon representative of the product, but not necessarily on the product itself. Hardness test limits normally apply to the product. In a perfect world the tensile test does represent the product, but that is not always the case. This is evident on castings...
That is why the source of hardness conversions should always be stated, and agreed on between contracted parties. Other countries have their own conversion equivalencies, as guided by their own standards professionals and administrators.
In homogenous materials the hardness will be the same. However, the effects of surface work hardening and surface compositional variances will influence the result either way because of the depth of penetration into the material. These effects obviously cannot be generalised in conversion...
I have a Chinese microhardness tester, and it took a while to set it up for accurate readings. The greatest problem I found was due to the error in the magnification, and hence the accuracy of the measurement scale. I used a stage micrometer to recalculate the actual magnification, and used this...