The HERMES spectrograph installed on the 1.2-m Mercator telescope has been used to monitor the radial velocity of 13 low-metallicity carbon stars, among which seven carbon-enhanced metal-poor (CEMP) stars and six CH stars. All stars but one show clear evidence for binarity. New orbits are obtained for eight systems. The sample covers an extended range in orbital periods, extending from 3.4d (for the dwarf carbon star HE 0024-2523) to about 54yr (for the CH star HD 26, the longest known among barium, CH, and extrinsic S stars). The period - eccentricity diagram for the 40 low-metallicity carbon stars with orbits now available shows no difference between CH and CEMP-s stars (the latter corresponding to those CEMP stars enriched in s-process elements, as are CH stars). We suggest that they must be considered as one and the same family and that their different names only stem from historical reasons. Indeed, these two families have as well very similar mass-function distributions, corresponding to companions with masses in the range 0.5-0.7M_{sun}_, indicative of white-dwarf companions, adopting 0.8-0.9M_{sun}_ for the primary component. This result confirms that CH and CEMP-s stars obey the same mass-transfer scenario as their higher-metallicity analogues, barium stars. The P-e diagrams of barium, CH, and CEMP-s stars are indeed very similar. They reveal two different groups of systems: one with short orbital periods (P<1000d) and mostly circular or almost circular orbits, and another with longer period and eccentric (e>0.1) orbits. These two groups either trace different evolutionary channels during the mass-transfer episode responsible for the chemical peculiarities of the Ba/CH/CEMP-s stars, or result from the operation of tidal circularisation in a more recent past, when the current giant star was ascending the first giant branch.