We explore a sample of 148 solar-like stars to search for a possible correlation between the slopes of the abundance trends versus condensation temperature (known as the Tc slope) both with stellar parameters and Galactic orbital parameters in order to understand the nature of the peculiar chemical signatures of these stars and the possible connection with planet formation. We find that the Tc slope correlates at a significant level with the stellar age and the stellar surface gravity. We also find tentative evidence that the Tc slope correlates with the mean galactocentric distance of the stars (Rmean), suggesting that stars that originated in the inner Galaxy have fewer refractory elements relative to the volatile ones. We found that the chemical peculiarities (small refractory-to-volatile ratio) of planet-hosting stars is probably a reflection of their older age and their inner Galaxy origin. We conclude that the stellar age and probably Galactic birth place are key to establish the abundances of some specific elements.