Coalbed gas (CBG) is a typical self-generated and self-stored gas and is one of the most ideal materials for studying the geological-geochemical models of natural gas and its source rock. However, studies show that CBG is usually a mixed gas consisting of thermogenic gas and secondary biogenic gas which make its original geochemical compositions change. We collected nine CBG samples and the corresponding coal samples from a coal core drilled in a CBG well in the Panxian Basin. The gas samples were measured using a MAT-271 trace-gas mass spectrometer for the molecular components and a Delta Plus XP stable isotope mass spectrometer for the carbon and hydrogen isotope values. The coal R-max values were measured by a LEICA DM2500P and MSP-II microscope photometer. The main geochemical characteristics of the CBG samples are as follows: CH4 concentrations from 97.28 to 95.16%, C-1/C1-n from 0.995 to 0.999; delta C-13(1) from -33.2 to -41.9 parts per thousand, delta D-CH4 from -170.6 to -123.5 parts per thousand, delta C-13(2) from -29.7 to -23.2 parts per thousand, and delta(CCO2)-C-13 from -24.6 to -20.0 parts per thousand. The characteristics reflect that Panxian CBG is a pure thermogenic gas, thus, it is more suitable for studying the geological-geochemical model system of thermogenic natural gas. Some important and new discoveries are presented in this paper: a discriminant system, delta C-13(1)-Delta delta C-13(CO2-C1), is proposed, which could be used to effectively distinguish between biogenic and thermogenic CBG, and the reasonable boundary values of delta C-13(1) and Delta delta C-13(CO2-C1) may be -50 parts per thousand and 25 parts per thousand, respectively; a series of models referring to isotope values, R-max, and depth, such as delta C-13(1) = 31.58R(max) - 100.02 (r = 0.913), delta D-CH4 = 248.68R(max) - 625.73 (r = 0.946), delta D-CH4 = 7.5228 delta C-13(1) + 148.2 (r = 0.990) and delta C-13(2) = 20.722R(max) - 66.596 (r = 0.681), were established for the first time; the carbon isotope fractionation degree of CBG components decreases with the increase in their relative molecular mass. The temperature and the molecular mass of CBG components play important roles in controlling the isotope compositions and variations of CBG. The models and the isotope fractionation laws may be more reliable and precise because of the self-generating and self-storing characteristics of CBG. The results have not only great application value in the fossil energy fields but also important scientific significance in gas geochemistry.