Recently, scientists and engineers are interested in coefficients of static friction on micro and nano scale. On macro scale, the friction force is proportional to load, the apparent coefficients of static friction are always constant and not related with the load and the contact area between the load and the substrate, which have been described as Amontons' laws. However, a lot of experiments carried out with scanning microscope, atomic force microscope and friction force microscope on micro or nano scale showed that Amontons' laws can not used successfully. On micro or nano scale, there is no general expression published in literatures to describe the relationship between the coefficients of static friction and the load. Also the published data do not compare with and discuss each other. In this paper, from the definition of differential coefficients of static friction, the expressions for differential and apparent coefficients of static friction, 〓 and 〓 for several models are deduced. Only 〓 can be measured in experiments, which can be the coefficients on micro or macro scale depending on the load on the substract, but 〓 can not be measured because the differential variables are too small to measure. In Amontons' model, 〓 equals to 〓 and both are constant. In single asperity model with load on micro or nano scale, 〓 and 〓 are not constant but propotional to P^-1. In the model based on absoption layers as third bodies between two contact bodies, 〓 is a constant, 〓 is not a constant but proportional to P^-1. 〓 is a constant only in high normal pressure. In the model based on constant P, 〓 and 〓 are related with F and A . Finally, the experimental data published in literatures have been discussed based on the novelly deduced expressions.