Context. Terrestrial-type exoplanets in or near stellar habitable zones appear to be ubiquitous. It is, however, unknown which of these planets have temperate, Earth-like climates or for example, extreme Venus-like climates. Aims. Technical tools to distinguish different kinds of terrestrial-type planets are crucial for determining whether a planet could be habitable or incompatible with life as we know it. We aim to investigate the potential of spectropolarimetry for distinguishing exo-Earths from exo-Venuses. Methods. We present numerically computed fluxes and degrees of linear polarization of starlight that is reflected by exoplanets with atmospheres in evolutionary states ranging from similar to the current Earth to similar to the current Venus, with cloud compositions ranging from pure water to 75% sulfuric acid solution, for wavelengths between 0.3 and 2.5 μm. We also present flux and polarization signals of such planets in stable but spatially unresolved orbits around the star Alpha Centauri A. Results. The degree of polarization of the reflected starlight shows larger variations with the planetary phase angle and wavelength than the total flux. Across the visible, the largest degree of polarization is reached for an Earth-like atmosphere with water clouds due to Rayleigh scattering above the clouds and the rainbow feature at phase angles near 40. At near-infrared wavelengths, the planet with a Venus-like CO2 atmosphere and thin water cloud shows the most prominent polarization features due to Rayleigh-like scattering by the small cloud droplets. A planet in a stable orbit around Alpha Centauri A would leave temporal variations on the order of 10-13 W m s-1 in the total reflected flux and 10-11 in the total degree of polarization as the planet orbits the star and assuming a spatially unresolved star-planet system. Star-planet contrasts are on the order of 10-10 and vary proportionally with planetary flux. Conclusions. Current polarimeters appear to be incapable to distinguish between the possible evolutionary phases of spatially unresolved terrestrial exoplanets, as a sensitivity close to 10-10 would be required to discern the planetary signal given the background of unpolarized starlight. A telescope or instrument capable of achieving planet-star contrasts lower than 10-9 should be able to observe the large variation of the planets resolved degree of polarization as a function of its phase angle and thus be able to discern an exo-Earth from an exo-Venus based on their clouds unique polarization signatures.