We present a fully differential chemical abundance analysis using very high resolution (λ/δλ >~ 85, 000) and very high signal-to-noise (S/N ~800 on average) HARPS and UVES spectra of 7 solar twins and 95 solar analogs, of which 24 are planet hosts and 71 are stars without detected planets. The whole sample of solar analogs provides very accurate Galactic chemical evolution trends in the metallicity range -0.3 < [Fe/H] < 0.5. Solar twins with and without planets show similar mean abundance ratios. We have also analyzed a sub-sample of 28 solar analogs, 14 planet hosts, and 14 stars without known planets, with spectra at S/N ~850 on average, in the metallicity range 0.14 < [Fe/H] < 0.36, and find the same abundance pattern for both samples of stars with and without planets. This result does not depend on either the planet mass, from 7 Earth masses to 17.4 Jupiter masses, or the orbital period of the planets, from 3 to 4300 days. In addition, we have derived the slope of the abundance ratios as a function of the condensation temperature for each star and again find similar distributions of the slopes for both stars with and without planets. In particular, the peaks of these two distributions are placed at a similar value but with the opposite sign to that expected from a possible signature of terrestrial planets. In particular, two of the planetary systems in this sample, each of them containing a super-Earth-like planet, show slope values very close to these peaks, which may suggest that these abundance patterns are not related to the presence of terrestrial planets.