We have compiled composition, luminosity, and binarity information for carbon-enhanced, metal-poor (CEMP) stars reported by recent studies. We divided the CEMP star sample into two classes having high and low abundances, respectively, of the s-process elements and consider the abundances of several isotopes, in particular, 12 C, 13 C, and 14 N, as well as the likely evolutionary stages of each star. Despite the fact that objects in both groups were selected from the same surveys (primarily the HK survey), without a priori knowledge of their s-process element abundances, we identify the following remarkable differences between the two classes: s-element-rich CEMP (CEMP-s) stars occupy a wide range of evolutionary states, but do not have a strongly evolved 13 C/ 14 N ratio, whereas s-elementnormal CEMP stars (CEMP-no) are found only high up the first-ascent giant branch and possess 13 C/ 14 N ratios approaching the CN cycle equilibrium value. We argue that these observational constraints can be accommodated by the following scenarios. CEMP-s stars acquire their distinctive surface compositions during their lifetimes when mass is transferred from an AGB companion that has recently synthesized 12 C and s-process elements. Such mass-accreting stars can be enriched at almost any stage of their evolution and hence are found throughout the H-R diagram. Dilution of transferred surface material as the accretor ascends the giant branch and its surface convective zone deepens may reduce the number of such stars, whose surfaces remain C-rich at high luminosities. Many, but not necessarily all, such stars should currently be in binary systems. Li-preserving CEMP-s stars may require a different explanation. In contrast, a CEMP-no star is proposed to have formed from gas that was enriched in 12 C from the triple-process in a previous generation of stars, some of which has been converted to 13 C and 14 N during the present star's giant branch evolution. The binary fraction of such stars should be the same as that of non-carbon-enhanced, metal-poor stars.