A: The two constants arise from different estimates of the average refraction of the Earth's atmosphere as it pertains to a line of sight taken with surveying instruments. Even though it is called the "curvature and refraction" correction, most equations assume the same (average) amount of curvature even though the Earth is an oblate spheroid. The estimates of this refraction vary from country to country and from research report to research report, so your manufacturer is probably attempting to cater to customs in different countries or other regional differences.
As it turns out, if you are using your total station for trigonometric leveling, these differences create very small, virtually imperceptible differences in the final result of a difference in elevation in most surveying situations. Where the results are different, the horizontal distance will have to be so large that the error from other sources will add more uncertainty than the discrepancy caused by incorrect selection of the constant. Users should be aware that the refraction of the atmosphere varies with density, and thus barometric pressure and temperature of the air. When doing trigonometric leveling over long distances or great differences in elevation, keep in mind that the effects of elevation on pressure and temperature are such that one end of the line or both ends will have refraction that is somewhat different from the "average" value used in the equation. Experts will tell you that changes in refraction become greater and practically unpredictable, sometimes even reversing in direction, when the line of sight passes within a few feet of the Earth's surface as well.