Faint high latitude carbon stars are rare objects commonly thought to be distant, luminous giants. For this reason they are often used to probe the structure of the Galactic halo; however more accurate investigation of photometric and spectroscopic surveys has revealed an increasing percentage of nearby objects with luminosities of main sequence stars. We analyzed new optical spectra and photometry and used astronomical databases available on the web, aiming at clarifying the nature of the ten carbon star candidates present in the General Catalogue of the Second Byurakan Survey. We verified that two stars are N-type giants already confirmed by other surveys. We found that four candidates are M-type stars and confirmed the carbon nature of the remaining four stars; the characteristics of three of them are consistent with an early CH giant type. The fourth candidate, SBS 1310+561 identified with a high proper motion star, is a rare type of dwarf carbon showing emission lines in its optical spectrum. We estimated absolute magnitudes and distances to the dwarf carbon and the CH stars. Our limited sample confirmed the increasing evidence that spectroscopy or colour alone are not conclusive luminosity discriminants for CH-type carbon stars.